This is a multi-part message in MIME format. ---------------0101260434298 Content-Type: text/plain; name="01-38.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="01-38.keywords" Wulff construction, surface tension, Kac model, crystal shapes ---------------0101260434298 Content-Type: application/postscript; name="rio.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="rio.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: rio.dvi %%Pages: 30 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips rio -o rio.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2001.01.19:1104 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (rio.dvi) @start %DVIPSBitmapFont: Fa cmtt9 9 18 /Fa 18 118 df<121E123FEA7F80EAFFC0A4EA7F80EA3F00121E0A0A728927>46 D64 D<3803FFC0000F13F04813FC487F487F81903880 7FC0383F001F001E6D7E000C1307C7FCEB1FFF90B5FC12075A5A383FFC07EA7FC0EAFF00 12FCA3140F7E007F133FEBC0FF6CB612806C15C07E6C13F36C13C1C69038007F8022207C 9F27>97 DI100 DII<153F90391FC0FF80D97FF313C048B612E05A5A4814CF3A1FF07FC7 C09039C01FC3809039800FC000003F80EB0007A4EB800F001F5CEBC01FEBF07F6CB55A92 C7FC485B5CEB7FF0EB1FC090C9FCA213A06CB5FC6C14E04814F848804880397F8001FF00 7EC7EA3F80007C140F00FC15C0481407A46C140F007EEC1F80D87F80137F3A3FF003FF00 6CB55A6C5C6C5C000114E06C6C1380D90FFCC7FC23337EA027>II<130F497E497EA46D5A6DC7FC90C8FCA7 383FFF80487FA47EEA000FB3A2003FB512E04814F0B612F8A26C14F06C14E01D2F7BAE27 >I<143C147E14FFA4147E143C1400A73801FFFE4813FFA47EC7123FB3AE147F003C137E 007E13FEB413FC1303EBFFF814F06C13E06C13C06C13803807FE0018407CAE27>I<397F 07C01F3AFF9FF07FC09039FFF9FFE091B57EA26C81390FF87FE19038E03F8001C01300A3 EB803EAF3A7FF07FC1FF27FFF8FFE3138001F913E7A201F813E3277FF07FC11300292081 9F27>109 D<387FE07F39FFF1FFC001F77F90B57E817E0003EB81FCEBFE005B5BA25BAF 3A7FFF81FFE0B500C313F014C7A214C36C018113E024207F9F27>II<393FFC03FC397FFE0FFF00FF013F13804A13C0 007F90B5FC6CB6FC39007FFE1F9138F80F809138E002004AC7FC5CA291C8FCA3137EAB00 3FB57E4880B6FCA27E6C5C22207E9F27>114 D<9038FFF3800007EBFFC05A5A5A5A38FF 801F38FE000F5AEC07806C90C7FCEA7F8013FC383FFFE06C13FC000713FF00011480D800 0F13C09038007FE0140F0038EB03F0127C12FC7E6C13079038C03FE090B5FC15C0158015 0000FB13FC38707FF01C207B9F27>I<131C133E137EA7003FB512F04814F8B6FCA36C14 F0D8007EC7FCAB1518153C157EA4017F13FE15FCEB3FC3ECFFF86D13F06D13E06D13C06D 1380903800FE001F297EA827>I<397FE01FF8486C487EA4007F131F00031300B1140114 03EBF80F90B612E06C15F07E7FEB3FFC90391FF07FE024207F9F27>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb msbm9 9 1 /Fb 1 77 df<007FB57EB6FC7E2603C0F0C8FC00015BB3AD1706170EA2171EA2173C177C 17FC1601EE03DCEE0F9CEE3F38000390387001FC007FB712F8B8FC7E2F337FB22D>76 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmbx9 9 11 /Fc 11 66 df48 D<143C14FC1303131FEA03FFB5FCA3EAFC1F1200B3B2007FB512FEA41F31 7AB02C>III<153F5D5DA25C5C5C5CA2 5C5C5C91B5FC14FBEB01F31303EB07E3EB0FC31483EB1F03133F137E13FC13F8EA01F012 03EA07E0EA0FC01380EA1F005A127E5AB712FEA4C700071300A80107B512FEA427317EB0 2C>I<000C140ED80FE013FE90B5FCA25D5D5D5D158092C7FC14FC14E001BCC8FC1380A5 EB83FC90389FFF8090B512E015F89038FC0FFC9038E003FE01C07F496C1380130016C0C7 FCA216E0A2120C123FEA7F8013C0EAFFE0A216C013C016806C485A01001400003E5C391F 800FFC390FE03FF86CB55A6C14C0C691C7FCEB1FF823327CB02C>II<123EEA3F8090 B612F8A416F04815E016C0168016005D5D007EC7FC007C495A4A5A48495A4A5A5D4AC7FC C75A147E147C14FC495AA21303A2495AA2130FA3495AA3133FA4137FA86D5AA2010FC8FC 25337BB12C>III65 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd msam8 8 3 /Fd 3 63 df<18201870A284A284D801C002707FD807E002FC7F486C496C1480D81E78D9 03CFEB03C0D83C3E903A0F878001F0486CD91F03B512FC28F007803C0114FE296003C078 007F13FCC66C6C4890380001F0902600FBE0EC03C0DA7FC0EC0780021FC81300020E150E 02045D91C95AA260A218203F197D9C47>32 D<17C01603160FEE3F0016FCED03F0ED0FC0 033FC7FC15FCEC03F0EC0FC0023FC8FC14FCEB03F0EB0FC0013FC9FC13FCEA03F0EA0FC0 003FCAFC12FC12F012FC123FEA0FC0EA03F0EA00FC133FEB0FC0EB03F0EB00FC143FEC0F C0EC03F0EC00FC153F0040EC0FC000F0EC03F000FCEC00FC003F153FD80FC0EC0F80D803 F0EC03C0D800FC1401013F91C7FCEB0FC0EB03F0EB00FC143FEC0FC0EC03F0EC00FC153F ED0FC0ED03F0ED00FC163FEE0F80EE03C016012A3B7AAB37>54 D<12C012F012FC123FEA 0FC0EA03F0EA00FC133FEB0FC0EB03F0EB00FC143FEC0FC0EC03F0EC00FC153FED0FC0ED 03F0ED00FC163FEE0FC01603160FEE3F0016FCED03F0ED0FC0033FC7FC15FCEC03F0EC0F C0023FC8FC14FCEB03F0EB0FC0013FC9FC01FC1580D803F0EC03C0D80FC0140F003FC8EA 3F00007C15FC00F0EC03F048EC0FC0C8003FC7FC15FCEC03F0EC0FC0023FC8FC14FCEB03 F0EB0FC0013FC9FC13FCEA03F0EA0FC0003FCAFC127C12F05A2A3B7AAB37>62 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmr5 5 1 /Fe 1 44 df<14E0B0B712C0A3C700E0C7FCB022237C9B2B>43 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmsy5 5 1 /Ff 1 1 df0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg eufm9 9 1 /Fg 1 83 df82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmsy9 9 6 /Fh 6 104 df<007FB712FCB812FEA26C16FC2F047A943C>0 D<17075F5F5F5F5FA25EA2 5EA25E83160F161EA2163CA21678167016F016E0030180ED03C0A2923807803FA2ED0F00 151EA25D157C15785D14015D4A5ADA07DFB57E92B6FC5C5CA2023CC7121F147C4A810010 5BEA3001267803E0140F387C07C0267F0F8081B5176091C8EBF9E049923807FFC06C4817 8049EEFE006C48ED03F8D81FC0ED01E0D8078092C8FC3B3A7EB53D>65 D<0260EB1FE0D901F0EBFFF8902607E00713FC011F011F13FE017F5B01FF9038FC07FF3A 01EFE1F00190398FE3C00027000FE780137F4AC7FC14DF02FE147E495A177C4A14F84A14 F0EE01E04AEB07C0013FEC0F804AEB3E00ED01FCED07F09138803FE090397F81FFFC4A13 FF4A14804A14C090267E000713E001FE1300EE3FF0161F49EC0FF816071201491403A312 035B17F0A2484815E0160717C04848EC0F8001C21500018F141E261FBF805B496C13F83A 3FFFF807F0D83E7FB512C0D87E3F91C7FCD87C1F13FC486C13E026E001FEC8FC30377EB4 32>II102 D<127EEAFFC013F0EA07F8C67E137E7F6D7EB3A66D7E A26D7E6D7EEB01FE9038007FE0141F147F903801FE00EB03F0495A495AA2495AB3A649C7 FC137E5BEA07F8B45A13C0007EC8FC1B4B7BB726>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmex9 9 1 /Fi 1 99 df<140C143FECFFC0497F010713F8011F13FE90397FE1FF803A01FF003FE0D8 03FCEB0FF0D80FF0EB03FCD83FC0EB00FFB4C8EA3FC000F8150700E015012A0E80B72B> 98 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj eufm10 10.95 2 /Fj 2 83 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmex8 8 1 /Fk 1 99 df<143014FCEB03FF010F13C0013F13F090B512FC0003EB03FF260FFC0013C0 D83FE0EB1FF0D8FF80EB07FC00FCC8FC00F0153C260C80B027>98 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmsy6 6 6 /Fl 6 84 df0 D<136013F0A30060136000F013F0EAFC63EAFE 67383FFFC03807FE00EA01F8EA07FE383FFFC038FE67F0EAFC63EAF0F000601360000013 00A3136014157B9620>3 D<14301438B1B712FCA3C70038C7FCAFB712FCA326277CA430> 6 D48 D<0107B512F0013F14FE48B7FC00071680390FC1F000 D81E01141F003C150F127C00785BEAF00300E0160000005D161E5E4A13F80107EB07F091 38C3FFC002C790C7FCEC8FFC010F5B1483EC01FC496C7EA2011E137F013E7F82013C9038 1FC006017C151E92380FE03C0178903807F0F801F8ECFFF0496D13C048486D130049EB00 FC2F237EA135>82 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmr6 6 4 /Fm 4 52 df<1438B2B712FEA3C70038C7FCB227277C9F2F>43 D<137013F0120712FFA2 12F91201B3A6B512E0A313217AA01E>49 DI< 13FE3803FFC04813E0380F03F0381E00F8003F13FC147C138013006C13FC000C13F8C7FC EB01F0EB03E0EB0FC03801FF00A2380003E0EB00F8147C147E143E143F127CA212FEA214 7E5A007813FC383E01F8381FFFF0000713C00001130018227DA01E>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmti10 10.95 55 /Fn 55 123 df11 DI< DC07FCEC7FF893273FFF8003B5FC93B5D8C00F14C0923D01FC07E03FC00FE0923D03F001 F07E0001F0922607C00349EB00F8030F902607F1F8130392281F800FF3F01307A2033F4A 5A93260007C715F04BD9038F15E0DD000FEC03C04E4890C7FC15FEA34E5AA24A5AA44EC9 FC4A5A0103BBFC5BA27F90260007F0C748C77E1BFEA34D5A4A484C5AA44D48495A4A5AA3 505A4D5A4A5AA2505AA24D5AA24AC792381FC0701CF0A34D4890383F81E014FEA2F383C0 604A023F021F13800101198797380F8F00F207FE4DC76C5A4948715A97C8FC177E5C17FE 01075DA2001E9038E07801003F02FC5B387F0FC100FF01C3495A02835C4C5A3AFE1F03F8 0F3BF81E01E01F80D87C3CD9F03ECBFC3A3FF800FFFC6C486D5AD807C0EB0FC0555383BF 50>14 D<15031507150E153C157815F0EC01E0EC03C014071580EC0F00141E143E5C5CA2 495A13035C495AA2495A131F91C7FC5B133E137EA25BA25B1201A2485AA3485AA3485AA3 121F5BA3123F90C8FCA45A127EA55AAE127CA6123C123EA2121EA27EA27E7F12036C7EA2 1200205A73C325>40 D<14031580EC01C015E0140015F0A21578A2157C153CA2153EA315 1E151FAD153FA7157EA515FE15FCA3140115F8A3140315F0A2140715E0A2140F15C0A2EC 1F80A3EC3F00A2147EA2147C14FC5C13015C495AA2495A495AA249C7FC131E133E5B5B5B 485A485A485A48C8FC121E5A5A5A12C0205A7FC325>I44 D<387FFFF8B5FCA414F01506789621>I<120FEA1F80EA3FC0 127F12FFA3EA7F801300123C0A0A77891C>I<181818381878A218F0170118E0EF03C0A2 EF0780A2EF0F005F171E5FA25FA25F16015F4C5AA24C5AA24CC7FC5E161E5EA25EA25E15 015E4B5AA24B5AA24BC8FC5D151E5DA25DA25D14015D4A5AA24A5AA24AC9FC5C141E5CA2 5CA25C13015C495AA2495AA249CAFC5B131E5BA25BA25B12015B485AA2485AA248CBFC5A 121E5AA25AA25AA21260355B7FC32E>I<15FE913807FF80021F13C091387F07F0ECFC03 903901F801F8903803E000010714FC495A4948137C167E49C7FC4914FE137E13FEA2485A A200031401A25B000715FCA2491303120FA34848EB07F8A44848EB0FF0A44848EB1FE0A3 16C090C7123F5A1680157FA2481500A215FEA25D1401485C14035D4A5A127C007E495A4A 5A6C49C7FC147E381FC1FC380FFFF0000313C0C648C8FC273F76BC2E>I<15031507150F 150E151E153E157E15FC14031407141F903801FFF8130FEB1FF314C390380E07F01300A3 EC0FE0A4EC1FC0A4EC3F80A4EC7F00A414FEA4495AA4495AA4495AA4495AA4495A497E00 7FB512E015F0B612E07E203D77BC2E>I<15FE913803FFC0020F7F91383F03F891387C00 FC02F0137E495A49487F495A91C713805BEB1E0CEB1C1CD93C0E14C013381378A213F017 80484848137FA35CD803C0ECFF005C4A485A12019039C3C003FC9039FF8007F86C01005B 017C495A90C7485A4B5A4BC7FC15FEEC01F8EC07F0EC0FC0EC3F80027EC8FC495AEB03F0 EB0FC0495A013EC9FC49141C49141E48485C5B485A48485C000F15F890C85AD81FE01301 01FF495A48EBF00FD83C7FB55AD8780F5C010391C7FC486C5B6D6C5A6E5A48EB07E02A3F 79BC2E>II<1638167C 16FC1501A4ED03F8A3ED07F0A316E0150FA216C0151FA21680153F16005D157EA25DA24A 5AA24A5AA24A5AA24A5A5D141F92C7FC5C143EEC7C0EECFC1F9138F83F80EB01F0903903 E07F00EB07C0A2EB0F8090381F00FE133E5B5B49485AEA01E0EA07C0EA0FFE391FFFC3F8 007F13FBB6FCD8F80114703AF0003FFFF80040130FC76C13E01600EC0FE0A44A5AA44A5A A44AC7FCA2143E141C264F7CBC2E>I<131E133FEB7F80EBFFC0A2481380A26C1300137E 133C90C7FCB3120F487E487E127F12FFA36C5A90C7FC123C122777A61C>58 D<173C177CA217FEA21601A216031607A2160FA2161FA2163DA2167916F916F1150116E1 923803C1FFA2ED0780A24B5A5D151E153E153C5DA25DA24A5A14035D14075D4AC7FC844A B6FCA25C5C0278C7127F14F85C495AA2495AA2495AA249C8FC5B131E133E017E8213FED8 07FF15FF007F01E0013FEBFF80B57E4A5B70140039417BC044>65 D<49B712C018F84916FE6D8290280003F8000113809438007FC0183F19E04A48141F19F0 A34A48140F181FA34A4815E0A2183F19C04A48EC7F8018FF4D1300604AC7EA07FC4D5AEF 1FE0EFFFC091B648C7FC17F817FF4AC77F4948EC1FE0717EA2717E4948811703A284495A A449485D1707A2604948140F60171F4D5A495A4D5A4D5A040390C7FC49C7485A49EC3FF8 007F90B65AB812C094C8FC16F83C3E7BBD40>II<49B812F8A25B7F90260003FC C7127F180FF003F0A24A481401A44A5A19E0A34A5A173CA2F003C04A481378180195C7FC 17F84A485B16011603160F91B65AA4903A01FE001FC01607A349485CF00780A2F00F0049 48EB0F00A2181E93C7FC4948153E183CA260495A18F84D5AA249484A5A1707170FEF3FC0 494814FF01FF140F007F90B75AB9FC95C7FCA23D3E7BBD3E>69 D<49B812F0A490260003 FCC7127F181FF007E0A24A481403A44A5A19C0A34A5AA2177094387807804A4813F01803 95C7FC1601DA7F805BA2160316079139FF001FC092B5FCA3495D9138FE003F160FA24948 91C8FCA44948131EA3161C494890C9FCA4495AA4495AA4495A497E007FEBFFE0B6FCA25D 3C3E7BBD3B>II<49B512FE4914FFA26D14FE90390003 FE005DA34A5AA44A5AA44A5AA44A5AA44A5AA44AC7FCA4495AA4495AA4495AA4495AA449 5AA4495AA4495A13FF007FEBFF80B6FCA292C7FC283E7BBD23>73 D<49B500FE90380FFFFE705B495C6D18FC90260003FEC7000313C04BEDFE0019F819E04A 484A5A4E5A061EC7FC187C4A485C4D5A4D5AEF07804A4849C8FC173E5F5F4A48485AEE03 C04C5A041FC9FC4A485A5E5E03817F4A5A5D92381F7FC0ED3E3F903801FE7C4B6C7EECFF E015C049496C7E15005C4A6D7E495AA2707EA2495A707EA28349487FA284177F495A717E A349488101FF4B7E007F9026FF8007B57EB64980611500473E7BBD46>75 D<49B67E83495D7F90260003FEC8FC5DA34A5AA44A5AA44A5AA44A5AA44A5AA44AC9FCA4 495AA4495A18C0EF01E0A24948EC03C0A217071880495AEF0F00A25F4948141E173EA25F 494814FC16014C5A160F4948133F01FF49B45A007F90B6FCB8FC5FA2333E7BBD39>I<49 B593380FFFF87017FC494E13F86D60D90003F0F800505AA21AF7DA07BF4B485AA2DB9FC0 EC03CFA2DA0F1F4B485AF10F1FA2191E021E4D5A193C1978A2023C4C48C7FC6F7EF001E0 F003C0027817FEF00780A2F00F0002F092381E01FCA2183C6F7ED901E04B485AA218F0EF 01E0D903C04C5AEF03C0A2EF0780D907804A48485AED03F8171EA2D90F004A495A5FA25F 011E4D5AEEF9E0EEFBC0A2496DB44849C8FCA294C7FC017C5C01FC17FED803FF4A130100 7F01F892B512FEB54A5A16F0DAF0005E563E7BBD52>I<902601FFFE91381FFFFE6F16FF 494C13FE6D82D900036D010013C0F17E00197C70143CDA07BF5DA2ED9FE0A2DA0F1F5D6F 7EA391261E07F8495AA36F7E023C4B5A821501A202786D495A81A2EE7F804A4BC7FCA2EE 3FC0A24948151EEE1FE0A349486D6C5AA3EE07F849485D17FC1603A249C76D5A1601A2EE 00FF011E5EA2177FA2495E173FA2137C01FC6F5AEA03FF007F13F8B5150F95C8FC4A8048 3E7BBD44>I<49B77E18F04916FC6D82903B0003FC0003FF05001380F07FC0183F4A48EC 1FE0A44A4815F0A319E04A48143FA319C04A48147FA21980F0FF004A5A4D5A4D5A4D5A4A C7485AEF3FE0933801FF8092B548C7FC4915F817E04ACAFCA2495AA4495AA4495AA4495A A4495AA4495A13FF007FEBFF80B6FCA292CAFC3C3E7BBD3E>80 D<92381FE00192397FFC 0380913A01FFFE070002076D5A91390FE03F9F91391F8007FF4A486C5A027C130114FC49 5A4A6D5A13035C13074A5C130FA3011F5DA35F94C7FC80A214F8EB0FFEECFFE015FC6DEB FF806D14E06D806D806E7F141F02037FEC003F1507ED01FF81A282A312077F48C8127EA4 485DA25E1501485D6D495A15076D5C007F4A5A6D49C8FCD87DF8137E3978FF01FC486CB4 5A6D13E0D8E00F5B26C001FEC9FC314279BF33>83 D<90B9FC5A5AA2913A001FE003FED8 07F8150001E0167E494948133E485AA290C7FC484A48133C121EA25A4BC7FCA25A18784A 5A5AA2C716004A5AA44A5AA44A5AA44A5AA44A5AA44A5AA44AC9FCA4495AA4495A497E00 3FB67EA4383D71BC41>I<147E49B47E010713C790390FC3EF8090391F00FFC0133E49EB 7F8013FC485A485A00071500A2485AA2001F14FE5B123FA24848485AA44848485AA49138 07F01C48153CA391380FE078127E141F023F13F0123E003F903877E1E0381F01E73A0F87 C3E3C03A07FF81FF806C01001300D800FC137C262977A72E>97 DII<167FED1FFF5DA3ED00 FEA4ED01FCA4ED03F8A4ED07F0A4ED0FE0A2147E903801FF8F0107EBDFC090380FC3FF49 C6FC133E49EB7F8013FC485A485A00071500A2485AA2001F14FE5B123FA24848485AA448 48485AA4913807F01C48153CA391380FE078127E141F023F13F0123E003F903877E1E038 1F01E73A0F87C3E3C03A07FF81FF806C01001300D800FC137C284077BE2E>II<167CED01FEED07FF92380F878017C0ED1F0FED3F1F 163F157F037E1380EE1F00EDFE0E93C7FCA24A5AA54A5AA54A5A0107B512F8825EA29026 000FE0C7FCA54A5AA64A5AA54AC8FCA514FEA5495AA413035CA4495AA4495AA3001E5B12 3F48485A12FF91C9FCA2EAFE3EEAF83CEA7878EA3FF06C5AEA07C02A5383BF1C>III<147014F8EB01FC1303A214F8EB01F0EB00E01400AD137C48B4FC481380 EA078F380E0FC0121E121C003C13E0007813C0131F127012F0EB3F80A212E038007F00A2 13FEA3485AA3485AA33807F01C143CEA0FE0A21478EA1FC0147014F014E01381380F83C0 EBC7803807FF006C5AEA00F8163E79BC1C>III IIII<903903E001F8903907F807FE496C487E903A1E3E3E0F80 903A3C3F7807C0017801F013E015E001709038C003F013F015803901E07F0017F8A21607 EBC0FEC7FCA217F04948130FA44948EB1FE0A317C04948133F1780A2EE7F004948137E6E 13FE5E4B5A011F495A02F85B4B5A9138FC1F8090263F9FFFC7FCEC8FFCEC83E00280C8FC 49C9FCA413FEA4485AA31203387FFFF0A2B5FC6C5B2D3A80A72E>I<023F1320903901FF 80F00107EBC1E090380FC1E390381F80F790383E007F4914C001FC133F485A1203484814 80A2485AA2001FEC7F005B123FA2484813FEA44848485AA44A5A5AA34A5A127E140F141F 003E495A003F137F6C13FF380F83EF6CB4485A6C131FEA00FC13004A5AA44AC7FCA414FE A3130190B512F8A4243A77A72A>IIII<137C48B41438486D137C260787C013FEEA0F07001E7F001C4A 5AEA3C0F123812784B5A38F01FC0A2EB3F8000E04A5A1200EB7F00A24B5A13FEA3484849 5AA4484890383F80E01681A392387F03C0A39238FF078012014A14003A00FC03BF0F9039 7E0F1F1E90393FFE0FFC6D486C5A903907F003F02B2979A731>I<017CEB03C048B4EB07 E0489038800FF0380787C0D80F07131F001E13E0001CEC0FF8D83C0FEB07F00038140312 78150138F01FC0A2EB3F8000E015E01200EB7F00A2ED03C013FEA34848EB0780A3ED0F00 485A150E151EA2151C5DA200015C15F06D485A0000495A90387E07806DB4C7FCEB1FFCEB 03F0252979A72A>I<017C16F048B491387001F8486D9038F803FC3A0787C001FCD80F07 1507001E13E0001C913903F803FED83C0FED01FC0038160012784B48137C38F01FC0A2EB 3F8000E04A4813781200EB7F00A24B4813F013FEA3484890393F8001E0A3EF03C04848EB 7F00A218801707A2EF0F005D0001161E4A141CD800FCEC803CDA03DF5B903A7F078FC1F0 903A3FFF07FFE090260FFE035B902703F8007FC7FC372979A73C>I<903907C007E09039 3FF00FF890397FFC3FFC9039F87E7C3E3A01E03EF01F2603C03F133F3A07801FE07FD80F 00EBC0FFA2001E013F13FEED807C4815381600A2003849C7FCC7FCA314FEA4495AA44948 131C163CA2001C1578387E07F012FF16F0010FEB01E012FED8FC1FEB03C03AF81CF80780 3A783CFC1F00397FF87FFE393FE01FF8390FC007E028297BA72A>I<137C48B41438486D 137C260787C013FEEA0F07001E7F001CEC01FCEA3C0F12381278ED03F838F01FC0A2EB3F 8000E0EC07F01200EB7F00A2ED0FE013FEA34848EB1FC0A44848EB3F80A4ED7F00A35D00 015C14013800FC03EB7E0F6DB45AEB1FFDEB07F1EB00014A5AA25D000E1307003F5C387F 800F5D4A5A1300007E49C7FC007C137E00785B387C01F8383E07E06CB45A6C90C8FCEA03 F8273B79A72C>I<02F81370D903FC13F0497E90390FFF01E049138149EBC3C049EBFF80 D97E071300EBF80049131E48485B6C485B90C75A4A5A4A5A4A5A4AC7FC141E5C5C5C495A 495A495A49C8FC131E49EB01C0491303A249EB0780485A4848130FD807FEEB3F00390FFF C0FE14FFD81F075BD83C035BD87C015BD878005B48EB7F80023EC7FC24297CA725>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo msbm8 8 4 /Fo 4 91 df66 D68 D82 D<000FB612FC5A3A183E00301801F0EB6030EA19C0001BC7EAC060001EEB01804815C000 3890380301801406ED03000030130C15060010495AC712305D14605D4A5AEB01805DEB03 004A5AD90603C7FC130C140613185C495A016014014A130313C04A130748485AD8030014 064948130E120649C7121ED80C06143612184914E64848EB01CCED070C4848133EB712FC 7E282E7EAD38>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi6 6 16 /Fp 16 121 df11 D I<137CD803FF131C48138048EBC03848EBE070EA3E01397800F0E00070137048EB79C014 39C71380143FEC1F00A3141EA2141CA4143CA214381478A45CA35C14401E217F9520>I< EB0FE0EB1FFE1330EB603E141C14001370A213787F133E7F1480A2EB0FC0EB7FE0EBF7F0 EA03C3380783F8EA0F01121F123E13005AA34813F0A2130114E0A2387803C0A2383C0780 001E1300EA0FFEEA07F817257EA31C>I<13031480EB0700A314FC14FE130FEB3CFCEB70 005B485A485A120790C7FC120E121E121C123C12381278A25AA77EA27E127F13E0EA3FFE 381FFF806C13C0000313E0EA003FEB07F0EB01E0A314C0EA01C13800FF80EB3E00172F7C A31C>16 D34 D<1238127C12FE12FFA2127F123B1203A31206A2120C121C12181270122008117B8613> 59 D<90B5EB3FFEA3D907E0EB1FC04948EB1E0016785EED03E090391F800780031FC7FC 153C5D90383F01E01403140F4A7EEB7E7FECF3F8EB7FE1EC81FCEBFF00497F49137E157F 48487F82151F824848130F826F7E3B7FFF803FFF80B5000014005D2F227DA133>75 D78 D99 DI<1338137CA2137813701300A7EA0780EA1FE01239EA31F0127112E1A2EAE3E01203 EA07C0A3EA0F80A2EA1F0C130E131C123E13181338EA1E70EA0FE0EA07800F237DA116> 105 D<140C141E143EA2141C1400A7EB07C0EB1FE0EB38F0EB70F813E0A2EA01C0A23800 01F0A4EB03E0A4EB07C0A4EB0F80A4EB1F00A21238EA783EEAF83C5BEA70F0EA7FE0EA1F 80172D81A119>I<001F01FE13FE3B3F83FF83FF803B73C707C707C09039EC03CC03D8E3 F801F813E001F013F0A201E013E000070107EB07C001C013C0A2EE0F80390F800F80A2EE 1F0C170E271F001F00131C163E17181738003E013EEB1E70EE0FE0001C011CEB07C02F17 7D9536>109 D<380F01F0383F87F83833CE1CEA73F83863F03C00E3137C13E014383807 C000A4485AA448C7FCA4123EA2121C16177D951D>114 D<3801F81E3907FC7F80390F1E E3C0381C0FC1003813C3003013871270EC8380C648C7FCA4133EA2EC0180003014C03978 7C038012F8EC070038F0FC0E3871DE1C387F8FF8381F03E01A177D9523>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmex10 10.95 39 /Fq 39 112 df<140E141E143C147814F014E01301EB03C0EB0780130F14005B133EA25B A25BA2485AA212035B1207A25B120FA3485AA4123FA290C7FCA25AA6127EA212FEB3A212 7EA2127FA67EA27FA2121FA46C7EA312077FA212037F1201A26C7EA2137CA27FA27F7F14 801307EB03C0EB01E0130014F01478143C141E140E176C72832A>0 D<126012F012787E7E120E120F6C7E6C7E7F12017F6C7EA2137CA27FA27FA21480130F14 C0A2130714E0A3EB03F0A414F8A21301A214FCA61300A214FEB3A214FCA21301A614F8A2 1303A214F0A4EB07E0A314C0130FA21480131F1400A2133EA25BA25BA2485A5B12035B48 5A48C7FC120E121E5A5A5A1260176C7C832A>I<150F157FEC01FFEC07FCEC1FE0EC3F80 EC7F0014FE495A495AA2495AB3AE5C130FA2495A495A49C7FCEA01FEEA03F8EA0FF0EA7F 8000FEC8FCA2EA7F80EA0FF0EA03F8EA01FEEA007F6D7E6D7E6D7EA2130780B3AE6D7EA2 6D7E6D7E147FEC3F80EC1FE0EC07FCEC01FFEC007F150F206C768335>8 D<127012FEEA7FC0EA1FF0EA07FCEA01FEEA007F6D7E6D7E6D7EA26D7EB3AE130380A26D 7E6D7E147FEC3F80EC1FE0EC07F8EC01FEEC007FA2EC01FEEC07F8EC1FE0EC3F80EC7F00 14FE495A495AA25C1307B3AE495AA2495A495A49C7FCEA01FEEA07FCEA1FF0EA7FC000FE C8FC1270206C768335>I<126012F0B3B3B3A31260043B73811E>12 D16 D<127012F8127C7E7E6C7E6C7E12037F6C7E6C7E137CA27F133F6D7E13 0F806D7EA26D7EA26D7EA26D7EA2147EA2147F8081141F81A2140F81A36E7EA36E7EA481 1401A381A21400A281A481A21680A8153FA216C0B3A71680A2157FA81600A25DA45DA214 01A25DA314035DA44A5AA34A5AA35D141FA25D143F92C7FC5C147EA25CA2495AA2495AA2 495AA2495A5C131F49C8FC133E5BA25B485A485A5B1207485A48C9FC123E5A5A127022A3 7D8336>I<17F01601EE03E0EE07C0EE0F80EE1F00163E5E5E5E15014B5A4B5A4B5A151F 93C7FC153E157E157C5D14014A5AA24A5A5D140F4A5AA24AC8FCA2147EA25CA2495AA213 035C13075C130FA25C131FA2495AA349C9FCA313FEA3485AA4485AA31207A25BA3120FA2 5BA2121FA45BA2123FA55BA2127FAA90CAFC5AB3AC7E7FAA123FA27FA5121FA27FA4120F A27FA21207A37FA21203A36C7EA46C7EA3137FA36D7EA36D7EA2130F80A2130780130380 1301A26D7EA2147EA280A26E7EA26E7E1407816E7EA26E7E1400157C157E153E8182150F 6F7E6F7E6F7E150082167C8282EE0F80EE07C0EE03E0EE01F016002CDA6D8343>I<1270 12F8127C7E7E6C7E6C7E6C7E6C7E12007F137C7F7F80130F6D7E8013036D7E806D7EA214 7E143E143F6E7EA26E7EA26E7EA26E7EA26E7EA281140081157E157FA28182A26F7EA36F 7EA36F7EA36F7EA46F7EA382A21500A382A282A21780A4163FA217C0A5161FA217E0AA16 0F17F0B3AC17E0161FAA17C0A2163FA51780A2167FA41700A25EA25EA31501A25EA34B5A A44B5AA34B5AA34B5AA34B5AA293C7FC5DA2157E15FE5D14015DA24A5AA24A5AA24A5AA2 4A5AA24AC8FC143E147E5CA2495A5C495A13075C495A131F91C9FC133E5B5B5B1201485A 485A485A48CAFC123E5A5A12702CDA7D8343>I21 D<1778EE01F81607161FEE7FE0EEFF80923803FE004B5AED 0FF04B5A4B5A4B5A4BC7FC4A5A4A5AA24A5AA24A5AA24A5AA34A5AB3B3B3A94A5AA44AC8 FCA25C1301495A5C13075C495A495A495A49C9FC13FE485AEA07F8EA0FE0EA3FC048CAFC 12FCA2127FEA3FC0EA0FE0EA07F8EA01FC6C7E137F6D7E6D7E6D7E6D7E801303806D7E13 0080A26E7EA46E7EB3B3B3A96E7EA36E7EA26E7EA26E7EA26E7E6E7E6F7E6F7E6F7E6F7E ED07FC6F7E923800FF80EE7FE0EE1FF816071601EE00782DDA758344>26 D<127012FCB4FCEA7FC0EA3FF0EA0FF8EA03FC6C7E6C6C7EEB3FC06D7E130F806D7E6D7E 1301806D7EA36E7EA36E7EB3B3B3A96E7EA3140F81A26E7EA26E7E1401816E7E6F7E153F 6F7E6F7EED07F8ED01FC6F7EEE7F80EE1FE0EE07F81601A21607EE1FE0EE7F80EEFE004B 5AED07F8ED0FE04B5A4B5A157F4BC7FC4A5A5D14034A5AA24A5AA25D141FA34A5AB3B3B3 A94A5AA34AC8FCA3495A5C1303495A495A5C131F495AEBFF804848C9FC485AEA0FF8EA3F F0EA7FC048CAFC12FC12702DDA758344>I[<173EA2177C17F8EE01F0EE03E01607EE0FC0 1780161FEE3F00167E16FE5E4B5A15035E4B5A150F5E151F4B5AA24BC7FCA215FE4A5AA2 14035D14075D140F5D141F5D143FA24A5AA292C8FC5CA2495AA2495AA3495AA3130F5CA2 131F5CA2133FA25C137FA25CA213FFA34890C9FCA45B1203A412075BA4120FA25BA4121F A35BA4123FA65BA3127FAB5BA212FFB3B3A4127FA27FAB123FA37FA6121FA47FA3120FA4 7FA21207A47F1203A412017FA46C7FA3137FA280A2133F80A2131FA280130FA2801307A3 6D7EA36D7EA26D7EA28081A26E7EA2141F81140F811407811403811401A26E7E157FA26F 7EA26F7E150F8215076F7E8215016F7E82167E82EE1F80160F17C0EE07E01603EE01F0EE 00F8177C173EA2>47 272 107 131 72 32 D[<127812F8127C7E7E6C7E7F6C7E12037F 6C7E6C7E7F137E7F80131F6D7E801307806D7EA26D7EA26D7E147FA281143F81141F8114 0F81140781A26E7EA2140181A26E7EA26F7EA36F7EA382151FA282150FA282A2150782A2 1503A282A36F7EA4811780A417C0167FA417E0A2163FA417F0A3161FA417F8A6160FA317 FCAB1607A217FEB3B3A417FCA2160FAB17F8A3161FA617F0A4163FA317E0A4167FA217C0 A416FF1780A417005DA44B5AA35EA21507A25E150FA25EA2151F5EA2153F5EA34B5AA34B C7FCA24A5AA25D1403A24A5AA25D140F5D141F5D143F5D147F92C8FCA214FE495AA2495A A2495A5C130F5C495A133F91C9FC137E13FE5B485A485A5B1207485A5B48CAFC123E5A5A 1278>47 272 125 131 72 I[27 272 104 131 53 I[27 272 127 131 53 I[<177CEE01FC1607160F161FEE7FF0EEFFE04B13804B 13004B5A4B5A4B5A4B5A4B5A5E15FF4A5B93C7FC5C5D1407A24A5AA25D141FA44A5AB3B3 B3B3A65D147FA35D14FFA25D5B92C8FCA2495AA2495AA2495A495A5C133F495A495A4890 C9FC485A485AEA0FF0485AEA7FC048CAFC5AA27EEA7FC0EA1FE06C7EEA07FC6C7E6C7E6C 7F6D7E6D7E131F806D7E6D7EA26D7EA26D7EA2817F81A2147F81A3143F81B3B3B3B3A66E 7EA4140F81A26E7EA214038180826E7F157F826F7E6F7E6F7E6F7E6F7E6F13806F13E0EE 7FF0EE1FFC160F16071601EE007C>46 272 115 131 73 40 D[<127812FE6C7E7F6C7E EA3FF86C7EEA07FE6C7E6C7F6C7F6D7E6D7E6D7E130F806D7E1303807F81A26D7FA2147F 81A46E7EB3B3B3B3A6141F81A3140F81A21407811403A26E7EA26E7FA26F7E6F7E151F82 6F7E6F7E6F7E6F7E6F1380EE3FC0EE1FE0EE0FF8EE03FC1601A21603EE0FF8EE1FE0EE3F C0EEFF804B13004B5A4B5A4B5A4B5A5E153F4B5A4B5AA24A90C7FCA24A5AA214075D140F A25D141FA35D143FB3B3B3B3A64A5AA45D14FFA2495BA292C8FC5B5C1307495A5C131F49 5A495A495A485B4890C9FC485AEA1FFC485AEA7FE0485A5B48CAFC1278>46 272 115 131 73 I48 D<127812F8127C7E123F 6C7E120F7F6C7E6C7EA26C7E6C7EA2137E137F7F806D7E130F801307806D7EA26D7EA26D 7EA2147FA2816E7EA2141F81140F81A26E7EA26E7EA2811401A2818082A2157F82A2153F 82A26F7EA3150F82A36F7EA3821503A38281A283A281A283A3167FA283A4163F83A5707E A683160FA683A31607A583A682A41880AD82A318C0B3A732A47D8250>I64 D<933801FFC0B3A71880A35EAD1800A45EA65FA5160FA35FA6161F5FA64C5AA55F 167FA45FA216FFA35FA25DA294C7FCA25D5EA315075EA34B5AA35E151FA34B5AA25E157F A25E15FFA293C8FC5C5DA214035DA24A5AA24A5AA25D141F5D143FA24A5A92C9FCA214FE A2495AA2495AA2495A5C130F5C131F495A91CAFC5B137E5BA2485A485AA2485A485A5B12 1F48CBFC123E5A5A127832A47D8450>III<007FBB12F8BC7EA3D87FE0C9000180003FEF00076C6CEF007F6DF00F FF000F19036C6C18006DF17F806C6C193F6CF20FC06C6D18076E18036D6C19E0013F1901 6D6C18006E19F0010F1A706D7E6E19386D6C19007F6D7F816E7E143F6E7E81140F6E7E81 6E7E806E7F826F7E153F6F7E82150F6F7E826F7E81815E167C16785E15014B5A4B5A5E4B CCFC151E153E5D15785D4A5A14034A5A4A5A92CDFC141E143E4A19384A19705C494819F0 01031AE0494818014948180391CC13C0011E1907013E190F49F11F8049197F4919FF4848 060313000003190F4848187F4848943803FFFE90CA48B5FC48BBFC48625ABCFC6C62555B 7B7F60>80 DII<0038180E007C181F00FEF03F80B3B3B3A86C187F6C19 00A36D5F003F606D1601001F606D1603000F606D16076C6C4C5A6D161F6C6C4C5A6C6C4C 5A6C6D4B5AD97FE0020390C7FCD93FF8EC0FFE6DB4EC7FFC6D9039F007FFF86D90B65A6D 5E01001680023F4AC8FC020F14F8020114C09126001FFCC9FC415B7B7F4C>II<007FBF12F8C07EA38B6C0180CB12036C6DDE0001806C6DF1000F0B01 14806C6DF2003F6C6D1B076C6D090113C0F6007F6C6DF43FE06C6D1C0F6FF307F06D1D03 6D6D1B016D6DF300F820786D6D1C3C6D6D1C1C6D6D1C1E200E6D7F6D6D1C076E6D1B00A2 6E7F6E7F82806E7F6E7FA26E7F6E7F6F7FA26F7F6F7F6F7FA26F7F6F7F83816F7F707FA2 707F707F707FA2707F707F707FA2707F717F8583717F717F61715B715B7190CDFC601700 4D5A604D5A4D5A4D5A4D5A173F4DCEFC177E5F4C5A4C5A4C5A160F4C5A5F4CCFFC167E5E 15014B5A5E4B5A4B5A4B5A4BD0FC5D15FE4B1C074A481C0E4A5A4A481C1E4A481C1C021F 1D3C4A481C7C92D012F8027E1C014AF403F049481C0749481C0F0107F51FE049481C7F4A 983801FFC049481B0749CF121F017E99B51280491B07000199B6FC48484FB7120090C0FC 48665A5A48665AC0FC6C66787F7B7F83>88 DII<933803FFF0047FEBFF800303B612F0030F15FC033F15FF92B812 C0020317F0020F17FC4A9026FE001F7F027F01C001006D7E4A48C8001F7F4901F803077F 4901E003017F4901806F6C7E4990CA6C7ED91FFCEF0FFE4948717E4948717F4948717F4A 834849727E4890CC6C7E49191F4848737EA24848737E491903001F87491901003F874985 A2007F1C80491A7FA400FF1CC090CE123FB3B3B3B3AF007EF31F80003CF30F005A7F7B7F 65>92 D<003C1B0F007EF31F8000FE1CC06C1B3FA26D1A7F007F1C80A26D1AFF003F1C00 A26D61001F63A26D1903000F63A26D19070007636D190F000363A26D191F000163A26D19 3F6C63A26E187F017F62A26E18FF013F97C7FCA26E5F011F61A26E1703010F61A26E1707 010761A26E170F010361A26E171F0101616E173F6D61A26F167F027F60A26F16FF023F95 C8FCA26F5D021F5FA26F1503020F5FA26F150702075FA26F150F02035FA26F151F02015F A26F153F6E5FA270147F037F5EA27014FF033F93C9FC705B031F5DA2701303030F5DA270 130703075DA270130F03035DA270131F03015DA270133F6F5DA2EF807F047F5CA2EFC0FF 043F91CAFCA217E1041F5BA217F3040F5B17FF705BA3705BA3705BA3705BA3715AA2173F 95CBFC170E5A7F7B7F65>95 D<15C0EC03F04A7EEC1FFE91387FFF8049B512E049EB3FF0 90390FFC0FFC90393FF003FF903AFF80007FC04848C7EA1FE0D807F8EC07F8D81FE0EC01 FED87F809138007F8000FEC9EA1FC000F8160700C01600321180C333>98 D104 DI<163CED01FC1507151FED 3FF0EDFFC04A1300EC03FC4A5A4A5A4A5A4A5A147F5D4AC7FCA3495AB3B3AC495AA3495A 5C130F495A5C495A49C8FC13FEEA03FC485AEA1FE0EA7FC048C9FC12FCB4FCEA7FC0EA1F E0EA07F86C7EC67E137F6D7E6D7E806D7E1307806D7EA36D7EB3B3AC6D7EA36E7E81143F 6E7E6E7E6E7E6E7E6EB4FC6E13C0ED3FF0ED1FFC15071501ED003C26A375833D>110 D<127012FE6C7EEA7FE06C7EEA0FFCEA03FEC67E6D7E6D7E6D7E6D7E8013076D7EA36D7E B3B3AC6D7EA36E7E143F816E7E140F6E7E6E7E6E7E6EB4FCED7F80ED1FE0ED0FF8ED03FC 15001503ED0FF8ED1FE0ED7F80EDFF00EC01FC4A5A4A5A4A5A141F4A5A5D147F4AC7FCA3 495AB3B3AC495AA3495A130F5C495A495A495A49C8FCEA03FEEA0FFCEA3FF0485AEAFF80 48C9FC127026A375833D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr msam10 10.95 4 /Fr 4 63 df<007FB912E0BA12F0A300F0CBFCB3B3B2BAFCA36C18E03C3E7BBD47>3 D32 D<1818187CEF01FCEF07F8EF1FE0EF7F8093 3801FE00EE07F8EE1FE0EE7F80DB01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC 1FE0EC7F80D901FEC9FCEB07F8EB1FE0EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECB FCA2EA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0EB07F8EB01FE9038007F80EC1FE0EC 07F8EC01FE9138007F80ED1FE0ED07F80060EC01FE00F89138007F8000FEED1FE0D87F80 EC07F8D81FE0EC01FED807F89138007F80D801FEED1FE026007F80EC07F8D91FE0EC01FC D907F8EC007CD901FE15189026007F801400EC1FE0EC07F8EC01FE9138007F80ED1FE0ED 07F8ED01FE9238007F80EE1FE0EE07F8EE01FE9338007F80EF1FE0EF07F8EF01FCEF007C 1818364878B947>54 D<126012F812FEEA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0EB 07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8ED01FE923800 7F80EE1FE0EE07F8EE01FE9338007F80EF1FE0EF07F8EF01FCA2EF07F8EF1FE0EF7F8093 3801FE00EE07F8EE1FE0EE7F80DB01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC 1FE0EC7F80D901FEC81218D907F8157CD91FE0EC01FCD97F80EC07F8D801FEC8EA1FE0D8 07F8ED7F80D81FE0913801FE00D87F80EC07F800FEC8EA1FE000F8ED7F800060DA01FEC7 FCC8EA07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB07F8EB1FE0 EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFC12F81260364878B947>62 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmmi8 8 41 /Fs 41 121 df<14FE903807FF80011F13E090387F03F09039FC01F8062601F800130E48 4813FC4848137C4848EB7E1C121F491438003F147F90C7EA3F705A16E0A200FE15C0A216 801600A3127E5D4A5A003E903803DF0E6C90380F9F8E3A0FC07E0F9C2607FFFC13FC6C90 38F007F83A007F0001E0271F7E9D2D>11 D<157F913801FFC0020713E091380F81F09138 3E00F8027813784A137C5C495A495A49C7FC16FC130E16F85BED01F0ED03E04914C09138 1FEF8091387FFF005D01707F91383FEF8091380007C0A249EB03E0A316F0485AA316E048 481307A316C00007140F1680151F1600486C133E5D6D5B390EF803F0391C7FFFE06D1380 D90FFEC7FC90C9FC5AA45AA45AA3263C80AE28>I<133FD9FFC0137000037F486D13E048 7F489038FC01C0EA3F803A3C003E038048131E4890380E070048130FEC070E5AC7139C14 0315B8A315F0A25DA35DA35DA31407A292C7FC5CA4141EA45CA214381410242C7F9D24> I<14F0EB03FF4913E04913F0EB0E0FEB1C07EC01E0EC00C0011E1300A27F80A26D7E8080 1303806D7EEB07FE131FEB7F7F13FCD801F013803803E03FEA07C0EA0F80001F131F1300 5AA2127EA3481400A25CA2143EA25C127C1478003C13F8003E5B6C485A6CB45A6C5BD801 FEC7FC1C317EAF1F>II<14301470A4EC7FE015F0ECFFF84913F0903803CFE09038078000010E C7FC131E5B5B5B12015B485A12075B120F90C8FC5AA2123EA35AA512FCA5127EA2127FEA 3FC013F86CB4FC6C13E06C13F86C7FC67F131FEB03FFEB007F8080A2141E1320EB783CEB 7FF86D5AEB07C01D3C7DAD1F>I<0103B512F0010F14F8133F90B6FC4815F03A03FC0FC0 003907E007E0380FC00301807F121FEA3F00A2127EA348495AA35D140F5D141F92C7FC00 7C133E5C6C5B381F03F0380FFFC06C5BD801FCC8FC251E7E9C28>27 D31 D<161CD801C0143E0003157FA24848158048C8FC000E ED3F00001E81001C81123C0038131C143E48150E147EA300F0017C5B4813FC163C6C4913 3816784A1370496C13F0D8F803495A397C0FFE07007FB65A02BF5B6C013F90C7FC391FFC 1FFE6C486C5A3907E003F0291F7F9D2C>33 DI<123C127EB4 FCA21380A2127F123F1203A312071300A2120EA25A123C12385A122009157A8714>59 D<15C01401A2EC0380A3EC0700A2140EA35CA35CA35CA35CA2495AA3495AA349C7FCA313 0EA25BA35BA35BA35BA3485AA2485AA348C8FCA3120EA35AA35AA25AA35AA25A1A437CB1 23>61 D<147F903801FFE0010713F890380F80FC90381E003E497F0138EB0F80137C017E EB07C013FE16E05B137890C7FCA216F0A2EB03FE90380FFF87013F13C7D97E0013E001F8 136F4848137F4848133F485A000F15C0485A123F168090C7FC5A16005D00FE147EA25DA2 5D1401007E5C4A5A003E495A4A5A6C013FC7FC380FC0FE3807FFF8000113E038007F8024 307DAE25>64 D<167016F8A215011503A21507A2150F151F82153B1579157115E1A2EC01 C11403ED81FEEC07011500140E5CA25C147814704A7FA249487F49B6FCA25B49C77E130E 5B178049143F137813705BA21203000F157FD8FFFC903807FFFE6D5B496D13FC2F2F7DAE 35>I<011FB6FC4915E06D15F8903A00FE0003FCEE00FE177FA24948801880A349481500 5FA217FE49485C4C5AEE07F04C5A4948EB7F8091B6C7FC16FC16FF903A1FC0003FC0EE0F E0707E1603494880A21601A249C7FC1603A25F01FE14074C5AA24C5A4848EC7F804CC7FC ED07FCB75A16C04BC8FC312D7DAC35>I<011FB6FC4915E06D15F8903A00FE0003FEEE00 FFEF3F80171F4948EC0FC0170718E0A24948EC03F0A4495AA449481407A4494815E0170F A218C04948141F1880A2EF3F0049C8FC177E5FA201FE4A5A4C5A4C5AEE1F8048484AC7FC 16FEED0FF8B712E0168003FCC8FC342D7DAC3A>68 D<92387FC003913903FFF807021FEB FC0F91397FC03E1F903A01FE00071ED903F8EB03BED90FE0EB01FED91F80130049C812FC 017E157C5B485A48481578A2485A120F491570001F163048481500A348CAFCA312FEA392 383FFFFCA39238003F80A2EE7F00127EA36C15FEA26C7E15016C6C5C6C6C1303D803F8EB 0F7C6CB4EB7E3C3A007FFFFC18011FEBE008010390C8FC302F7CAD37>71 D<90271FFFFC03B51280495C6D80010090C7381FE0004A5DA349484A5AA449484AC7FCA4 494814FEA44948495A91B6FCA3903A1FC00003F8A44948495AA449C7485AA401FE4A5AA4 48484A5AA3B539F01FFFFEA202E05C392D7DAC3A>I<90261FFFFC90381FFF804917C06D 1780010090C73807F8004A15E0EF0F80051EC7FC49485C17F04C5AEE03804948010FC8FC 161E163816F04948485AED0380030FC9FC5D4948487E15FF02E17FECE39F90391FCF1FE0 ECDC0F02F87FECF007D93FC07FEC8003A26F7EEB7F006F7EA2167F13FE83163F83484814 1F8383B5D8F001B5FCA214E03A2D7DAC3C>75 D<011FB5FC5B6D5B010090C8FC5CA3495A A4495AA4495AA4495AA4495AA44948EB01801603A2EE070049C7FC5E160E161E01FE141C 163C167C5E484813011507ED3FF0B7FC5EA2292D7DAC30>I78 D<011FB512F849ECFF806D15E0903A00FE000FF0EE03F8EE00FC83494814 7EA4494814FEA34C5A495A4C5A4C5A4C5A4948EB1F8004FFC7FC91B512FC16E049809138 C003F86F7E6F7E495A167FA349C712FEA401FE495AA3EF018048481503A2EF0700B539F0 00FE1EEE7FFC4A6D5AC9EA07E0312E7DAC35>82 D<0007B8FC5AA23B1FE003F8007F0100 151E121E5A0038495AA248161CA24A5A5AA34849481318C71500A34A5AA44AC8FCA414FE A4495AA4495AA4495AA2130F000FB512F048805D302D7FAC29>84 D<267FFFE090381FFF80B5FC6C5BD803FCC73803F80049EC01E04C5A5F6D4AC7FCA20001 150E161E161C5E16786D14705E000014015E4B5A15076D91C8FC150E6D131E151C5DA25D 6E5AA290383F81C0EC8380A20287C9FC14CF14CEEB1FDC14FC5C5CA25C5C130F5C91CAFC A2312E7CAC29>86 D<0103B612F85B17F0903A0FFC000FE002E0131F0280EB3FC049C7EA 7F80011EECFF00011C495A013C5C0138495A4B5A49495A4B5A153F0160495A90C748C7FC 4A5A4A5A5D4A5A4A5A4A5A4A5A147F4AC8FC495A494813064A130E495A49485B495A495A 49C7123C49143848481478485A48485C491301484813034848EB0FE04848137F48B6FCB7 5AA22D2D7CAC30>90 D<140FEC3F80EC7FC014F114E11301EB03C11307148190380F8380 A2EB1F03A290383F0700133EEB7E0EA2EB7C1C13FC5CA248485A14F05CEBF9C048485A13 F791C7FC13FE5B5B485A5BA35B120F121F123F127300E3148039C3E001C00003EB078000 01EB0F00143E3800FBF8EB7FF0EB3FC01A307FAE1D>96 DI99 DI<147CEB03FF49139C90381F83FEEB3F01EB7E005B4848137E15FC485A 1207A29038E001F8120FA3391FC003F0A4EC07E0A2120F140FEC1FC00007133F3803E0FF 3801FFEF6CEBDF80EB3F1F1300A2EC3F00A31238007C137E00FE5BA238FC03F8EB0FF038 7FFFC06C90C7FCEA0FF81F2C7F9D22>103 DI<1307EB0F80EB1FC0A21480A2EB0E0090C7FCA8EA 01E0EA07F8487EEA1E3E1238A2EA707EA212E05BA21240EA01F8A3485AA2485AA214C0EA 0FC1A2EA1F81EB8380A2EB8700A2EA0F8E13FC6C5AEA01F0122E7EAC18>I<15E0EC03F0 A21407A2EC03E0EC01C091C7FCA814F8EB03FE497E90380F0F80131C013C13C013381370 EC1F8013E0A213409038003F00A4147EA45CA4495AA4495AA4495AA338380FC0127C38FE 1F8091C7FCEAFC3E13FCEA7FF86C5AEA1F801C3B81AC1D>II<2707 C007F013FE3C0FF01FFC03FF80281FF87FFE0F7F3C3CFCF83F1F07E03C387DE01FBC03F0 26707F8013F0A2020013E0D8E0FE14C0491480A21240D801F84948485AA34D5A4848137E A24D5AF081804848491483EF3F03A2F0070048484848137E180E173E183C48484848EB1F F8000F01016E5A6CC748EB07C0391F7E9D3E>109 D<39078007F0390FE03FFC486C487E 3938F8F83F9038F9C01F2670FF80138014005BEAE1FCA25B1241D803F0EB3F00A3157E48 5AA25D161848481438EC01F8A21670391F8003F0A2020113E0EDF1C048C7EAFF806CEC7F 00000E143E251F7E9D2B>I<3807803F390FE0FF80D81FF113C03838FBC19038FF83E048 1307EBFE0F13FCD8E1F813C01580EC0700004190C7FCEA03F0A4485AA4485AA4485AA448 C8FC7E120E1B1F7E9D20>114 DI117 DI<013F137C9038FFC1FE48EBE3FF3A 03C1F787803A0701FE07C0D80E00130FECFC1F5AD901F8138000381500150E001091C7FC C6485AA4495AA31503391C0FC007123E127F150ED8FE1F131E00FC141CD8783F5B903873 E0F0393FE1FFE0D81FC05B260F803FC7FC221F7E9D28>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmsy8 8 16 /Ft 16 113 df0 D<123C127E12FFA4127E123C08087A9414>I< 131EA2131F131EA30070EB0380007C130F00FEEB1FC0007FEB3F80EB9C7F390FEDFC0038 03FFF0C613C0013FC7FCEBFFC0000313F0380FEDFC397F9C7F80EB1E3F00FEEB1FC0007C EB0F8000701303000090C7FCA3131F131EA21A1D7C9E23>3 D<140381B3A3B812FCA3C7 D80380C7FCB3B812FCA32E2F7CAD37>6 D<170EA383A3717EA2717E841700187084181E 84F007C0007FB912F8BA12FC6C18F8CBEA07C0F00F00181E183860601701604D5AA24DC7 FCA3170EA33E237CA147>33 D<137813FCEA01FEA4EA03FCA313F81207A213F0A2120F13 E0A3EA1FC0A21380A3EA3F00A3123E127EA2127CA212FC5A12780F227EA413>48 DI<91B512C01307131F49C8FC13F8485AEA03C0485A48C9FC120E5AA25AA25AA35AA3B7 12C0A300E0C9FCA31270A37EA27EA27E120F6C7E6C7EEA01F06C7E133F6DB512C0130713 00222B7AA52F>I<9039038003FC010FEB0FFF013F013F138001FF90B512C048903983F0 7FE03A03DF07C01F90391F0F000F26003F1E13075C4A14C014F84AEB0F804A14004A131E 017F147C4A5BED03E09138001FC003FFC7FCEBFE03020F13E04A13F849487F9138001FFE 4848EB03FF1500EE7F8049143FA20003151FA25BA21207491500A2000F153E5B5ED81F98 1478017C5C01FEEB07E03A3FFFC03FC0003E90B5C7FC486C13FCD8783F13E0D8E00790C8 FC2B2F7EAD2E>66 DI<91B512F0010F14FF013F 15E090B712F82703FC3E017FD807C09038001FFE260F007EEB03FF001E03001380003E16 7F48EE3FC00078161F4817E048017C140FC7FC02FC1407A45CA2010116C0A24A140F1880 1303EF1F005C173E13074A5C1778010F5D4A495A4C5A011F4A5A91C7001FC7FC163E013E 14F8ED03F0017EEB1FC090267C03FFC8FC90B512FC4814F04814804801F0C9FC332D7EAC 37>I75 D<91B6FC010F15F0013F15FC 90B77E3B03FC3E001FFFD807C01401260F007E9038007F80001E163F123E48161F12785A 48017C1500C7FC02FC143EA25F4A14785F01014A5AEE07C0EE1F804A01FEC7FCED3FF801 03EB7FE0EDFF8002E17FECE03F01076D7E4A6C7EA2010F6D7EEC800382011F130102007F 03001403496E130F013E6E131FEF803E4991383FC07CEFE1F84991381FFFE07013C04848 6E130001C0EC03F8382E7EAC3C>82 DI<12E0B3B3B3AD034378B114> 106 D<18031807180F180E181CA21838A21870A218E0A2EF01C0A2EF0380A2EF0700A217 0EA25FA25F177817705FA24C5AA24C5AA24CC7FC136001E0140EEA03F000075D487E003F 5DEA79FC00F15DEA60FE00005D137F4B5A90383F80035E6D6C48C8FCA290380FE00EA26D 6C5AA26D6C5AA26D6C5AA26D6C5AA2EC7FC0A26E5AA26EC9FCA2140EA238427C823B> 112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmsy10 10.95 37 /Fu 37 111 df<007FB812F8B912FCA26C17F83604789847>0 D<121E123FEA7F80EAFF C0A4EA7F80EA3F00121E0A0A799B19>I<1506150FB3A9007FB912E0BA12F0A26C18E0C8 000FC9FCB3A6007FB912E0BA12F0A26C18E03C3C7BBC47>6 D<007FB912E0BA12F0A26C 18E0C8000FC9FCB3A6007FB912E0BA12F0A26C18E0C8000FC9FCB3A915063C3C7BAC47> I15 D<1818187CEF01FCEF07F8EF1FE0EF7F80933801FE00EE07F8EE1FE0EE7F80DB01FE C7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB07F8EB1FE0 EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFCA2EA7F80EA1FE0EA07F8EA01FE3800 7F80EB1FE0EB07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8 ED01FE9238007F80EE1FE0EE07F8EE01FE9338007F80EF1FE0EF07F8EF01FCEF007C1818 1800AE007FB812F8B912FCA26C17F8364878B947>20 D24 D<0203B612F8021F15FC91B7FC4916F8D907FCC9FCEB1FE0EB3F80017ECAFC13F8485A48 5A485A5B48CBFC5A121E5AA35AA35AAA1278A37EA37E121F7E6C7E7F6C7E6C7E6C7E137E 7FEB1FE0EB07FC6DB712F8010016FC141F020315F8363678B147>26 D<0060140C00F8141F6C81007FEC0FE0D81FC0EB03F8D80FF0EB01FED803F8EB007FD800 FEEC1FC0D93F80EB07F0D91FE0EB03FCD907F0EB00FED901FCEC3F80D9007FEC0FE0DA3F C0EB07F8DA0FE0EB01FCDA03F8EB007FDA00FEEC1FC0DB7F80EB0FF0DB1FC0EB03F8DB07 F0EB00FEDB01FCEC3F806FB4EC1FE0DC3FC0EB07F8DC0FE0EB01FCDC03F8EB007FDC01FE EC3FC09326007F80EB0FF0DD1FC0EB03F8DD07F0EB00FE716C147F0501153FDD07F014FE DD1FC0EB03F8DD7F80EB0FF005FEC7EA1FC0DC03F8EC7F00DC0FE0EB01FCDC3FC0EB07F8 4CC7EA0FE0DB01FCEC3F80DB07F002FEC7FCDB1FC0EB03F84B48495A03FEC7EA1FC0DA03 F8027FC8FCDA0FE0EB01FCDA3FC0EB07F84AC7EA0FE0D901FCEC3F80D907F002FEC9FCD9 1FE0EB03FCD93F80EB07F001FEC7EA1FC0D803F8027FCAFCD80FF0EB01FED81FC0EB03F8 007FC7EA0FE000FCEC1F804892CBFC0060140C503C7BB45B>29 D<19301978A385A385A2 85A2737EA2737E737E86737E1A7C8686F20FC0F207F0007FBB12FCBDFCA26C1AFCCDEA07 F0F20FC0F21F001A3E62624F5A624F5A4F5AA24FC7FCA2191EA261A361A3193050307BAE 5B>33 D41 D49 D<0203B512E0021F14F091B6FC4915E0D907FCC8FCEB1FE0EB3F8001 7EC9FC13F8485A485A485A5B48CAFC5A121E5AA35AA35AA3B812E017F0A217E000F0CAFC A31278A37EA37E121F7E6C7E7F6C7E6C7E6C7E137E7FEB1FE0EB07FC6DB612E0010015F0 141F020314E02C3678B13D>I<176017F0A2EE01E0A2EE03C0A2EE0780A2EE0F00A2161E A25EA25EA25EA24B5AA24B5AA24B5AA24BC7FCA2151EA25DA25DA25DA24A5AA24A5AA24A 5AA24AC8FCA2141EA25CA25CA25CA2495AA2495AA2495AA249C9FCA2131EA25BA25BA25B A2485AA2485AA2485AA248CAFCA2121EA25AA25AA25AA212602C5473C000>54 D<0060EE018000F0EE03C0A20078EE0780A36CEE0F00A36C161EA26C5EA36C6C5DA36C6C 5DA26C6C4A5AA36CB75AA36D5D0178C712076D4AC7FCA36D141EA36D5CA26D6C5BA36D6C 5BA26D6C485AA36D6C485AA39138780780A26E48C8FCA3EC1E1EA36E5AA2EC07F8A36E5A A36E5AA26E5A324180BE33>56 D<007FB612FEB8FCA27EC9120FB3A7001FB7FC5A5A7EC9 120FB3A8007FB7FCB8FCA26C15FE283F7BBE33>I65 D<020E14FF023E010713E002FE01 3F13F0010391B512F8010F010314FC013F4914FE903A7FFC1FE07F01FF90393F000FFFD8 01F3017E7FD800C3497F903807FDF8DAFFF07F4B14FEA25D4B14FCEF03F84990C7FC18F0 4AEC07E0EF0FC04AEC1F80EF7F004948EB01FCEE0FF8EE3FE09139F001FF80150F013F01 3F13F04A4813FC92B57E02E18002C1158090277FC0003F13C0040713E04A13017013F017 7F49C8EA3FF8A2171FA24848150FA4484816F0A34916E00007161F18C0491680000F163F 491600D9E1C0147E261FC7E05CD9DFF0495A263FFFFCEB07F0903ABFFF807FC0007F91B5 5A011F4AC7FCD87E0F14F8486C14E0D8F80191C8FC39E0003FF038427CBF3C>II<92B512FE020FECFFF0027F15FC 0103B87E010F83013F17F0D97FE00100802601FE0002077F2603F00102017FD807E09238 003FFFD80FC0701380001F17077213C0D83F804980007F7113E01300007E187F00F80103 17F00060183FC75BA2191FA214075DA21AE0A24A5AA2193F1AC04A5A1A80A2F17F004A5A 19FEA24B4A5A027F5E180392C85B4A4B5A4E5A4A4B5A01014CC7FC187E4A4A5A0103ED03 F04A4A5AEF1FC0010703FFC8FC4AEB03FE010FEC3FF89139E007FFE049B61280017F02FC C9FC48B612F04815804802F8CAFC6C91CBFC443E7FBD46>I71 D<4AB41638021F6D15F891B56C140101036E1403010FEF07F049170F90267FC07F16E090 38FC003F4848171F484818C04848173F48485C001F198049177F123F48C7007F1600007E 6000F85D006060C81501A203FF5D93C71203A34E5A4A5AA261180F4A5A027FB7FC49B85A 13075BA2F0BFC090260007F0C7123F140FA24B4A5A141FA25D023F15FF96C7FC5D147FA2 92C75A5C605C13011A044A0203143E0103187EF101FC5C01079338FF03F84AEEFFF01AE0 494817804A6EEBFE0049C913F8010CEE7FC047427FBD4D>I<0207ED03F0021FED1FF802 7FED7FFC4948EC01FF0107030713FE011FED1FF049ED3F80499238FE007E01F9DA03F813 7C01614A481378D901FED91FC013604CC8FC167EED01F80103495A4B5AED0F804A48C9FC 153E5D5D903807FDF014FB5D14FFA2EB0FF7A381EB1FE7A214E381EB3FC3A2ECC1FC1481 137FEC80FE14005B157F5B000181153F824848131F8249130F82000702071518496E143C 000F0203157C7014FC496D6C14F8001F17016F6C14F04991397F8003E0003F9338C00FC0 4991393FF07F8070B5120048C86C13FC007E6F13F0486F13C00070DB00FEC7FC3F427DBF 45>75 D<0470F0018004F818031501030319071D0F70181F0307193F1E006565705F6415 0F525A1C0F70171F1C3F4B187FED1E7F525A71ED01FBF303F3033CEF07E3043FEE0FC783 F31F87037894383F07F8041F167E7115FC03F0EE01F80803130F040F16F071EC07E0DA01 E0DC0FC05BF21F80706CEC3F00DA03C0167E08FE131F020701035D03806D495A4F5ADA0F 004B5A706C495A4F485C021E163F706C49C7FC023E16FE023C4B48143F94387F83F84AED 87F0F0CFE002F891383FDFC04AEDFF807190C8FC49485D715AD810035E263807C06E5A00 7C5F267F0F806E48EEF0E0B5C86C4816F394CAEBFFC0491C80761300491BFC6C48F20FF0 6C48F207C06C4897C8FCEA07C063457DBF6D>77 D<92B67E020F15FC027F15FF0103B812 C0010F17F0013F83D97FE0D9003F7F2601FE0002017F2603F0016E6C7ED807E0161FD80F C01607001F7113804B80EA3F80127F010082007E130312F800604A1600C7FCA261020715 014B5DA24E5A61020F15074B5D4E5A4E5A4EC7FC4A48147E4D5AEF07F0EF3FE0913A3FC0 03FF809226C1FFFEC8FC03C713F8039F13E0DA7FBF138004F8C9FC16804ACBFCA35C1301 A25C1303A25C13075CA2130F5C131FA25C133F5CA249CCFC137C137041437FBD3F>80 D<92B612E0020F15FF027F16E00103B812F8010F83013F83D97FE0D9000F7F2601FE00EC 007F2603F001030F7FD807E01603D80FC082121F4B80EA3F80127F010095C7FC007E1303 12F8006060C74914016161180302075E4B4A5A4E5A4E5A4EC8FC4A4814FEEF03F8EF3FF0 93381FFFC091261FE07F90C9FCEEFFFC03E113F003E37FEC3FC39238C07FFC161F4B6C7E 147F707E15004A6D7FA24A7F010182824A811303716CEB03C04A170F0107033FEC1F804A 6FEB3F00716C137E010F18FE4A9238FE01F8011F92390FFF87F04A6EEBFFE01A8049486E 91C7FC91C86C13FC017E6F13F00138043FC8FC4A407FBD4D>82 DI 86 DII<0060EE018000F0EE03C0B3B3A5 0078EE0780A26CEE0F00A26C161E001F163E6C6C5DD807E04A5AD803F8EC07F0D801FEEC 1FE03B007FE001FF806DB6C7FC010714F8010114E09026001FFEC8FC32397BB63D>91 DI<157FEC03FF141FEC3FE0EC7F80ECFE00495A495AA2495AB3AA495A A2495A5C017FC7FC13FEEA07FCEAFFF0138013F0EA07FCC67E137FEB1F80806D7EA26D7E B3AA6D7EA26D7E6D7EEC7F80EC3FE0EC1FFF1403EC007F205B7AC32D>102 D<127EEAFFE013F8EA07FEC67EEB3F806D7E6D7EA26D7EB3AA6D7EA26D7E1300147EEC3F 80EC1FE0EC07FF14011407EC1FE0EC3F80EC7E005C1301495AA2495AB3AA495AA2495A49 5A01FFC7FCEA07FEEAFFF813E0007EC8FC205B7AC32D>I<126012F0B3B3B3B3B1126004 5B76C319>106 D<0060131800F0133CB3B3B3B3B000601318165A75C32D>I<126012F0A2 1278A37EA37EA37EA36C7EA36C7EA36C7EA36C7EA31378A37FA27FA37FA36D7EA36D7EA3 6D7EA36D7EA31478A380A380A380A26E7EA36E7EA36E7EA36E7EA31578A381A381A381A3 ED0780A3ED03C0A2ED0180225B7BC32D>110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmmi10 10.95 57 /Fv 57 127 df11 DIII<4A7E1403A6EDBFE0EDFFF8A25C91381F7FF091383C3FC04AC7FC5C495A 495A495A49C8FC131E133E133C5B5BA2485A12035B12075B120F90C9FC5AA2123EA35AA4 12FC5AA77EA47E7E7E13C0EA3FF013FC6CB47E6C13F06C13FE6C6D7EC680013F7F010F7F 01017FEB003FEC07FC1401A21400A35DA201185B90381C01E090381F83C06DB45A010390 C7FCEB00FC25527CBE28>16 DI<14E0D903F0EB01C0EE03E00107EC 07F0A34948EB0FE0A44948EB1FC0A44948EB3F80A449C7EA7F00A401FE14FEA448489038 01FC031707A30003913803F80EA21507171C0007140F6D131D037913389026FF81F01370 489039FFE07FF001E79038803FE0903AE1FE000F8001E0C9FC485AA4485AA448CAFCA412 FEA35AA21270303C7EA737>22 D26 D<020FB512FE027F8049B71280010716005B013F5D90277FE0 3FE0C7FC9038FF000FD801FC6D7E484813034980485A120F491301121F485A150390C7FC 5AA300FE4A5AA34B5AA25E48141F5E6C4AC8FC127E157E003E5C003F495A6C495A390F80 0FC03907E03F802603FFFEC9FCC613F8EB3FC031287DA634>I<011FB61280017F15C048 B712E04816C05A481680261F800EC8FCEA1E0048131E5A1270485BA2C7FC147CA21478A2 14F8A3495AA31303A3495AA3130FA25CA2131FA3495A6DC9FC130E2B287DA628>I<137E 2601FFC01520486D157026070FF015E0260E07F8EC01C06EEC0380D81C03ED0700260C01 FE140E0000161E6D6C5C17385F6E6C5B4C5A023F495A6F48C7FC160E021F5BEDE03C1638 020F5B6F5AEDF1C0913807F38003FFC8FC5D5D1403A31401A24A7E1407140E4A7E5CEC78 7F02F07F14E0EB01C049486C7EEB0700130E496D7E5B5B01F06D7E485A496D7E485A48C7 6C6C5A000EEE0380489238FE070048140148913800FF0E48ED7FFC0060ED1FF8C9EA07F0 343B7EA739>31 D<0120ED01C00170ED03E001F8ED07F049150F484816F8120349150748 48150318F048C91201A2000E1600121E001C1430003C027814E0003814F81401A248EE01 C0A24A5A1703188000F05C170718004B5B170E0207141E6C496C5B021F147C6C496C5B6C 9038FFF8013B7F87FDFF0FF0D9FFF9EBFFE002F05C6C5B6C496C5B6C496C48C7FC6C4848 6C5AD801F8EB07F035297EA739>33 DI<121E12 3FEA7F80EAFFC0A4EA7F80EA3F00121E0A0A798919>58 D<121E123FEA7F80EAFFC0A313 E0127F123F121E1200A5EA01C0A3EA0380A212071300120EA25A5A5A12200B1C798919> I<1818187CEF01FCEF07F8EF1FE0EF7F80933801FE00EE07F8EE1FE0EE7F80DB01FEC7FC ED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB07F8EB1FE0EB7F 80D801FECAFCEA07F8EA1FE0EA7F8000FECBFCA2EA7F80EA1FE0EA07F8EA01FE38007F80 EB1FE0EB07F8EB01FE9038007F80EC1FE0EC07F8EC01FE9138007F80ED1FE0ED07F8ED01 FE9238007F80EE1FE0EE07F8EE01FE9338007F80EF1FE0EF07F8EF01FCEF007C18183636 78B147>II<126012F8 12FEEA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0EB07F8EB01FE9038007F80EC1FE0EC 07F8EC01FE9138007F80ED1FE0ED07F8ED01FE9238007F80EE1FE0EE07F8EE01FE933800 7F80EF1FE0EF07F8EF01FCA2EF07F8EF1FE0EF7F80933801FE00EE07F8EE1FE0EE7F80DB 01FEC7FCED07F8ED1FE0ED7F80DA01FEC8FCEC07F8EC1FE0EC7F80D901FEC9FCEB07F8EB 1FE0EB7F80D801FECAFCEA07F8EA1FE0EA7F8000FECBFC12F81260363678B147>I<5C5C A44A7EA84A7EA300F0163CD87F80EC07F8D83FFE9038C1FFF0000FB712C000031600C615 FC011F14E001071480010149C7FC9038007FF8A34A7EA2903801FCFEECF87E49487E4948 6C7EECC00F49486C7EEC0003011E6D7E011C1300013C8001381470498001601418014014 082E2C81AC2D>I<15FF020713E0021F13F891383F01FC913878003F02E0EB1F804948EB 0FC04948130749C713E049EC03F014C06EEB01F8497E17FCA25C4A14FE6D5A90C8FCA6EC 1FFEEC7FFF49B51283903903F801C390390FE000E34948137349C7123B017EEC3FFC13FE 4848141F485A000716F8A2485A001F16F05B123FA2EE3FE0485A17C0A2167F48481580A2 EEFF005EA290C7485AA26C4A5A5E4B5A6C6C130F4B5A001F4A5A6C6C49C7FC9038E001FE 3907F807F86CB55AC614C06D90C8FCEB0FF82F437CC030>II<91B712F84916FF19E08590260001 FCC7EA3FF8F00FFC727E727E4A4880A21A80A24A5AA44A48160060A24E5A4A485D4E5A18 1F4E5A4A48EC7FC04E5ADD03FEC7FCEF1FFC4AB612E095C8FC18E092C7EA0FF802FEEC03 FE717E717F727E495A727EA3494882A449485E187FA261494815FF615F4D90C7FC49484A 5A4D5A4D5A4D5A4948ECFFE0017F02075B007FB8C8FCB812FC17F06C93C9FC413E7DBD45 >II<91B712F84916FF19C019 F090260001FEC76C7EF00FFCF003FE727E4A486E1380197FF13FC0A24A48ED1FE0A21AF0 A24A48150FA31AF84A5AA3191F4A5AA31AF04A5A193FA34AC913E0197FA21AC0494816FF A21A806049481700A24E5A6149481507614E5A181F49484B5A614E5A4EC7FC4948EC03FE 4D5A4D5AEF3FE0494849B45A017F020F90C8FC007FB712FCB812F017C06C03FCC9FC453E 7DBD4B>I71 D<49B6D8803FB512F0A31BE0D9000190C8383FE0004B5EA34A484B5AA44A484BC7FCA44A 484A5AA44A484A5AA44A484A5AA44AB75AA44AC8EA1FE0A449484B5AA449484B5AA44948 4BC8FCA449484A5AA449484A5AA449484A5A496C4A7E007FB5D8E00FB512F8B64980A203 C05D4C3E7DBD4C>I<037FB512E092B6FCA218C09239001FF0005FA34C5AA44C5AA44CC7 FCA44B5AA44B5AA44B5AA44B5AA44B5AA44B5AA44B5AA3EA0F80486C49C8FC487E127F4A 5AEAFFC05DEB800349485A007C5C0078495A6C495A003EEB7F80261F81FEC9FC6CB45A00 0313F0C690CAFC33407ABD32>74 D<49B66C90387FFFF01BF896B512F085D9000190C838 0FFE004B16F01A804FC7FC4A48153C6119E0F003C04A484A5A060EC8FC6018784A485CEF 01C04D5A050FC9FC4A48131C5F17F04C5A91383FC0031607161F4C7E91387F807F923881 EFF8ED83C792388707FC9138FF0E03153C4B6C7E15E04901C07F4B7E92C77F4A147F495A 717EA2844948141F84170FA249486E7EA28417034948811701A284494882496C4A7F007F B500E0013F13FFB65CA24B5D4D3E7DBD4D>I<49B612E0835FA2D900010180C7FC4BC8FC A34A5AA44A5AA44A5AA44A5AA44A5AA44A5AA44AC9FCA4495A1804180EA24948151CA218 3C1838495A1870A218F0494815E01701A2EF03C049481407170FEF1F80177F4948EB01FF 017F021F1300007FB8FCB9FC5FA2373E7DBD3E>I<49B54AB512F082A27016E0D9000192 39000FFC00F103F0DBDFE015C019019126039FF04A5A158F821587DA07074BC7FC821503 82DA0E01150EA26F7EA24A6E5B167F83163F4A5E83161F834A010F5CA2707EA24A6E5B16 0383160149484B5A17FF821881494891387F8380A2EF3FC3A249C801E7C8FC171F18F717 0F010E16FEA21707A2496F5AA21701133C017C5ED803FF1500007F13FCB5167818704A15 304C3E7DBD49>78 D81 D<49B77E18F818FF8590280001FE000113E09438003FF0F00FF8727E4A5A727EA34A4881 A44A484A5AA34E5A4A5A614E5A4E5A4A484A5A4E5A4D48C7FCEF0FFC4A48EB7FF092B612 8005FCC8FC5F9139FF0001FEEE007F717E717E4948140F84A3494881A44948141FA44948 143FA44948027F5BF10380A2F107004948143F496C160E007FB500E0131FB66F5A050F13 784B6DB45ACA00015B9438003F8041407DBD45>I<003FB500F090387FFFFEA319FC2600 3FE0C7000313804A913800FE0018F8187849485DA449C8485AA448484B5AA448484B5AA4 48484BC7FCA44848151EA448485DA448485DA448485DA490C8485AA2484B5A7E4C5AA24C C8FC161EA26C6C5C5E001F4A5A6C6C495A6DEB0FC06C6CEB3F802703FE01FEC9FC6CB55A 6C6C13F0011F13C0D903FECAFC3F407BBD3E>85 DI<023FB712F05CA219E0DAFFFCC7EA3FC003C0EC7F8092C8EAFF 00D901FC5C4A4A5A4A4A5A49484A5A4A4A5A604A4A5A01074B5A91C848C7FC4C5A010E14 034C5A4C5A494A5A010C4A5A90C85B4C5A4CC8FC4B5A15034B5A4B5A4B5A4B5A5E4B5A4B C9FC4A5A4A5A14074A4814704A5A4A5A4A485C5D4AC8FC49484A5A495A13074948140349 485D49481407495A4A4AC7FC49C85A48485D4848157E000716FE484814034848140F4848 ECFFFC48B7FCA2B85AA23C3E7BBD3E>90 D<151EED7F80EDFFC0EC01E1EC03C191380780 E0140F15005C91383E01C0A2147CA214F80101EB0380A2EB03F0ED0700A2EB07E0150E13 0F4A5AA2011F5BA24A5A133F5DEC81C0EB7F014A5A4AC7FCA2EBFE0E5C5C1478EBFC7000 015BEBFDC0EBFF8091C8FC5B5B5BA412031207120F121F123D127900F014030060EC0780 0000EC0F000178131E017C1378013C5BEC03E090381FFFC06D90C7FCEB07FC23417FBF26 >96 DI99 DII<16 3EEEFF804B13C0923803E1E0923807C3F0ED0F87ED1F8F169FED3F1FA2037F13E0EE0FC0 EE0780037EC7FC15FEA54A5AA54A5A0103B512FE5BA25E90260007F0C7FCA54A5AA64A5A A54A5AA54AC8FCA514FEA5495AA45C1303A35CA2380F07E0EA3F87127FEBC7C0EAFF87EB 8F80130F4848C9FCEA7C1EEA783CEA3FF86C5AEA07C02C537CBF2D>III<147814FC1301EB03FEA2EB07FCEB03F814F0EB01E090C7FCAC13FC487E487E38070F 80000E13C0121C003813E0A21270EB1FC0A212E0EB3F80A212C038007F00A213FEA3485A A3485AA33807F00C141CEA0FE0A21438EA1FC01470A214E0A2380FC1C0EBC7803807FF00 6C5AEA00F8173E7DBC1F>III109 DII<91383F80089138FFE03C0103EBF0789039 0FE0F8F890381F803990383F001F017E14F049130F485A12034914E01207485AA2001FEC 1FC05B123FA24848EB3F80A448C7EA7F00A415FE5AA3007E495AA214036C13074A5A6C13 1FEB803F380FC1F36CB4485A000113C738007E0713004A5AA44A5AA44A5AA3147F90383F FFFEA4263A7DA729>113 DII<137C48B4140E48 6D131F26078FC0EB3F80EA0E07001C7F0018ED7F00EA380F1270A216FE48485AA3484848 485A1200EB7F00A24B5A13FEA34848495AA4484890380FE0181738A392381FC070A30001 023F13E0157F6D13EF00000101EBC1C0903A7E07C7C38090393FFF03FF6D486C13009039 03F8007C2D297DA734>117 D<017C14E048B4EB01F04890388003F83A078FC007FCEA0E 07001C13E01503D8380F130100701400167CA248485A163CA24848481338120049C7FCA2 167013FEA21660484814E0A2ED01C0A2485AED0380A2ED0700A2150E5D12015D6C6C5B5D 90387F03C06DB45A010F90C7FCEB03F826297DA72C>I120 D<137C48B4140E486D131F26078FC0EB3F80EA0E07001C7F0018ED7F00EA380F1270A216 FE48485AA3484848485A1200EB7F00A24B5A13FEA34848495AA44848495AA44B5AA30001 143F4B5A6D13FF00005BEB7E076DB46CC7FCEB1FFEEB03F890C7FC15FEA25D001F1301D8 3F805B387FC0035D4A5A49485A01005B007E49C8FC0070133E6C13FC383E03F8381FFFE0 00071380D801FCC9FC293B7DA72D>I<16C0ED01E0A3ED00F016F8167C007FB612FEB8FC A26C15FEC8EA01F8ED03F0ED07C0ED0F801600151E150C281270C02D>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmti9 9 57 /Fw 57 124 df11 D<923801FF80030F13F0033F 13F892387E007C03F8131E4A48133E4A48137F020714FE5D020F147C173817004A5AA54A C8FCA4011FB612E04915F06D15E09039007E0007A34AEB0FC0A4EE1F80495AA3EE3F00A2 495AA2167EA217184948141CEEFC38A44A1470010F14F816FCEE7CE0EE3FC04A131F011F EC0F0093C7FCA291C9FC5BA2EA1C3E123EEA7F3C137CEAFE78127CEA78F0EA3FE06C5A6C CAFC304582B42B>I<1338137C13FEEA01FC13F8EA03F0EA07E0EA0FC0EA1F80EA3E0012 3C5A5A12C00F0E66B327>19 D39 D44 D<387FFF80B5FCA31400110579921B>I<12 0E123FEA7F80A212FFA21300127E123C0909788818>I50 DI<137813FCEA01FE1203A213 FCA2EA01F8EA00E01300AE120E123FEA7F80A212FFA21300127E123C0F20789F18>58 D<161C163CA2167C16FCA21501821503A21507150F150E151CA21538A2157015F015E0EC 01C0A24A487EA24A487EA2140E141E141C5CA25CA25C130191B6FC5BA249C7EA7F80163F 130E131E131C133C13385BA25B12011203D80FF0147FD8FFFE90380FFFFEA217FC2F367B B539>65 D<0107B612E04915F86D15FE903A001FC000FFEF3F804A4814C0171F18E0A24A C7FCA402FE15C0173FA2EF7F804948150017FE1601EE03F84948EB0FF0EE3FE091B61280 94C7FC4915C09139F0001FE0EE07F0707E4948801601A283495AA449485C1603A24C5A49 C7FC4C5A4C5A4C5A01FE4A5A4CC7FC0001EC03FE007FB612F8B712E06C92C8FC33337CB2 36>II<0107B612E04915F86D15FE903A001FC000FFEF 3F804A48EB1FC0EF0FE0EF07F017034AC713F81701A218FC14FEA4495AA4495A1703A349 4815F81707A3494815F0170F18E0A24948EC1FC0A2EF3F80A24948EC7F00177E17FE4C5A 49C7485A4C5A4C5A4C5A01FE4AC7FC16FE0001EC07FC007FB612F0B712806C02FCC8FC36 337CB23A>I<0107B712E05B7F903A001FC0001F17074A4813031701A34AC713C0A414FE 160EA34948011C138094C7FCA2163C49485BED01F891B5FCA2495CECF0011500A249485B A217061707903A1FC001C00E1500EE001CA249485CA21778177049C812F05F1601160301 FE4A5A161F00014AB45A007FB7FCB8C7FC7E33337CB234>I<010FB71280A3903A003F80 007F171F4AC7120F1707A302FE1500A4495AA2163016384948EB700694C7FCA216F04948 5B1501150791B5FC495CA2ECE0071503D91FC05BA4494848C8FCA392C9FC49CAFCA413FE A4485AA21203B512FCA25C31337BB232>I<92391FE001809238FFF8030207EBFE07913A 1FF01F0F0091393F80079F9139FE0001FF495AD903F06D5A495A4948147E495A49C8127C 5B13FE5B00011678485AA2485A000F1670A2485A94C7FC5B123FA3485AA490CBFC92383F FFF8484A7F6F5B9238007F8094C7FC7EA216FEA37E4B5A7F121F6D1303000F5D6C6C1307 6C6C131ED801FCEB3C783A00FF01F83090397FFFE010011F0180C8FCD903FCC9FC313775 B43B>I<0107B512804914C06D14809039001FC000A24A5AA44AC7FCA414FEA4495AA449 5AA4495AA4495AA4495AA4495AA449C8FCA413FEA21201387FFFF8B57E6C5B22337CB21E >73 D<91381FFFFEA39138003FC0151FED3F80A4ED7F00A415FEA44A5AA44A5AA44A5AA4 4A5AA44A5AA44A5AA2123E127F4AC7FC5A147E4813FE485B38E001F86C485A387007E038 3C1FC0381FFF806C48C8FCEA03F027357AB228>I<0107B5398007FFF04917F86D17F090 28001FC00001130018FC4A4814F0EF03C04D5A050EC7FC4AC75A5F17F04C5A02FEEB0380 4CC8FC160E163C494813705E4B5A1507903803F80F4B7E153F4B7E903807F1E7ECF3C791 38F703F814FEEB0FFC4A6C7E14E08290381FC000A2167FA2495A707EA2707E49C7FCA270 7EA201FE81A2000182267FFFF890B57EB549806C6E5C3D337CB23B>I<010FB512C0A25E 9026003FC0C7FC5D4AC8FCA414FEA4495AA4495AA4495AA4495AA4495AA2EE018017C049 48EB0380A2EE0700A249C7FC160EA2161E01FE141C163C167C5E4848130115070003EC3F F0B7FC5EA22A337BB230>I<902607FFE0EDFFFC495E7F9026001FF0913803FE00A2023B 4B5A180EA2181C0273ED1DF818391871A2DAE1F84A5AA2EF01C3EF0383D901C1ED87E0EF 0707A2170ED903814A485AA21738EC80FCD907004A485AA217E0EE01C0010E4CC7FCEE03 80A2EE070049020E137EA2ED7E1CA2494A5B5EA25E494B5AED7FC01680A201F04A485A00 0180D807F8013E1307287FFF803C01B512C0B55C6CEC380146337BB245>I79 D<0107B612C04915F86D81903A001FC001 FEEE007F4A48EB3F80EF1FC0A34AC713E0A402FEEC3FC0A318804948147F18005F5F4948 495A4C5AEE0FF0EE3FC049B6C7FC16FC16E002F0C9FC495AA4495AA4495AA449CAFCA413 FEA21201387FFFF8B5FC7E33337CB234>I<0107B6FC4915E06D15F8903A001FC007FCEE 00FE4A48137FEF3F80A34AC713C0A402FEEC7F80A3EFFF00495A5F4C5A4C5A4948495AEE 1FE0EEFF8091B548C7FC4914F85E9138F001F86F7E4948137EA2167FA2495AA449485BA3 5E90387F0001A218C018E001FEED01C0A20001EE0380397FFFF800B591387F0F006CED3F FEC96C5AEE03F033357CB238>82 D<913901FC018091380FFF034A138791397E07CF0091 38F800EFD901E0137F495A4948133E130F91C7FC5B011E143C133EA3017E1438A393C7FC 137FA214C0EB3FF8ECFF806D13F06D13FC6D7F6D7F7FD9003F7F14039138007FC0151FA2 150FA3120C120E485DA393C7FC003C5C151E153E003E143C007E5C007F5C6D485A397BC0 03C039F1F80F8000E0B5C8FCEB3FFC38C00FF029377AB42B>I<0007B8FC5AA2903AF001 FC007FD81F80151F49485A001E160E5AA20038495AA248161E171C4A5A5AA34849481318 C71500A34A5AA44AC8FCA414FEA4495AA4495AA4495AA4495AA2131F003FB512F0A33033 73B237>I<263FFFFC90387FFF804892B5FC6C81C648C73807F000EE03C0485A5FA34848 4AC7FCA44848140EA448485CA448485CA448485CA448C85AA400FE4A5AA34B5AA25A4BC8 FCA2150E5DA2007E5C5D003E5C6CEB03C0390F800F802607E03FC9FC3803FFFC6C13F038 003F80313571B239>III97 D<133EEA0FFF485A120FEA007EA25BA4485AA4485AA4485AEBE1F0EBE7FCEBFFFE380FFE 1F9038F80F8013F001E013C0EA1FC0138015E0A2EA3F00A315C0007E131FA4007CEB3F80 12FC15005C147EA2007C5B5C495AEA3C03383E07E0381E0F806CB4C7FC6C5AEA01F01B35 78B323>I<14FE903803FF80010F13C090383F83E0EB7E00EBF803000113073803F00FEA 07E0000F14C09038C00780001F90C7FC5B123FA248C8FCA4127E12FEA3127E1520157015 E0003EEB01C0003FEB07806CEB1F00380FC0FE3807FFF86C13E0C66CC7FC1C2279A023> III<151FED3FC0EDFFE0EC01F1EDE3F0EC03E7 1407EDC7E016C091380FC380EDC000A24A5AA54AC7FCA490381FFFFE497F6D5BD9007EC7 FCA35CA6495AA5495AA5495AA5495AA45C131FA391C8FCA25BEA1C3E123EEA7F3C137CEA FE78127CEA78F0EA3FE06C5A6CC9FC244582B418>I<141FECFFC04913E7903907E0EF80 90380FC07FEB1F8090383F003F013E1400137E5BA20001147E5B1203A248485BA449485A A2120F12074A5AA21407A20003495A141F3801F07F3800FFF76D485AEB1F8FEB000FA24A 5AA4001C49C7FC123E007F137E147C00FE13FC387C01F8EB07E0383FFFC06C90C8FCEA03 FC21317DA023>III<153815FCA21401A2EC00F815701500AA143E14FF491380903803C7C090 380707E0EB0E031407131CA21338A29038700FC013301300A2EC1F80A4EC3F00A4147EA4 5CA4495AA4495AA4381C07E0123E387F0FC05CD8FE1FC7FCEA7C3EEA787CEA3FF86C5AEA 0F801E4283B118>II<131F3807 FF804813007EEA003FA2137EA45BA4485AA4485AA4485AA4485AA4485AA448C7FCA4127E A21318131C485AA45B12F812FCEA7CE0EA3FC06C5A6CC7FC113579B314>I<2703E003F8 137F3C07F00FFC01FF80280FF83FFF0713E03B1C7C7C1F0F83903B7EF00F9E01F026387F C013B8028001F07F1270020013E0017E14C0A248484948485A12601200A248484948485A A34D5A4848137EA294381F818019C0484849EC8380EF3F03A2F0070048484848133E180E A2183C48484848EB1FF8000F01016E5A6CC748EB07C03A227AA03F>I<3903C007F0390F E01FFC6D487E391CF8F81F2638FDE0138090387FC00FD9FF8013C04813005B5BA2D8E1F8 EB1F8012611201A24848EB3F00A3157E485AA2EDFC18161C48481438EC01F8A21670D81F 8013F0166016E0EDF1C048C7EAFF806CEC7F00000E143E26227AA02B>I<14FE903803FF C0010F13E090383F83F090387E00F84913FC4848137C4848137E485A120F5B001F147F5B 123F157E48C712FEA4007EEB01FC12FE15F81403007E14F0140715E0EC0FC0003EEB1F80 003FEB3F006C137E380FC1FC3807FFF06C13C0C66CC7FC202279A027>I<010F133F9039 3F80FFC002C113E0903973E7C1F09039E3FF01F89038E1FE00D9E3FC13FC3801C3F85CA2 16FE48485A1201EA000716FC90380FC001A490391F8003F8A216F01507D93F0013E0A2ED 0FC0168090397F801F00153E6E5AECE1F89038FCFFF0EC7FC06EC7FC91C8FC485AA4485A A4485AA2EA7FFFB57E91C8FC273080A027>I<903801F00C90380FFC1C90381FFE7C9038 3E0EF8EBFC07EA01F8EBF003D803E013F01207EA0FC0A2001FEB07E01380123FA2397F00 0FC0A4007EEB1F8012FEA3EC3F00A2127E5C14FEEA3E011303EA1F0F6CB45AEA07FCEA01 F0C7FC495AA4495AA4495AA248B5FC158015001E3079A023>I<3903C01F803907E07FE0 390FF0FFF0391CF9E07838387FC0EC80FCEBFF013970FE03F813FCEC01F0EC00E0D8E1F8 130012611201A2485AA4485AA4485AA4485AA448C8FC7E120E1E227AA020>II<130E131F5BA3137EA4 5BA4485AA2B512E014F014E03803F000A3485AA4485AA4485AA448C7FCA214C014E0387E 01C0A2EB0380A2EB0700127C130EEA3E3CEA3FF86C5AEA07C0143079AE19>III<01F81570D803FC010E13F8486C90381F01FCD80F 1F133F001C150316010038150049017E137C1270173C137E00E04A13381260C65AA24A48 1370EA01F8A34848484813E0A3EE01C0A201E013E0EE0380EBF0079238F00700140F0001 150E3A00FC3CF83C90397FF87FF86D486C5A90390FC00FC02E227AA033>I<011F137C90 387FC0FE9038FFE1FF3A01E1F38780390380FF073A0700FE0FC0151F000E9038FC3F805A ED1F00150E484848C7FC12181200A2495AA4495AA215061507391C0FC00E123E127F5DD8 FE1F5B12FCD8783F5B903873E1E0393FE1FFC0D81FC05B260F803EC7FC22227CA023>I< EA01F0486C130E486C131FD80E3E133F121C12181238017E137E1270A25B00E014FC1260 EA01F8A2EC01F8EA03F0A33907E003F0A4EC07E013C0A3EC0FC0EBE01F0003133FEBF0FF 6CB512806C13DFEB3F1F1300EC3F00A2000E133E003F137E147C4813FC5C387E01F0387C 03E0387807C0383C1F80D81FFFC7FCEA0FFCEA07F020317AA025>I<903807801CEB1FC0 90383FE03890387FF0789038FFF87048EBFFE09038F07FC03803C00F9038800380EC0700 C7120E5C5C5C5C495A495A49C7FC130E5B5B491360491370484813E0485A38070001390F F003C09038FE0F8048B5FCD83C1F130038380FFE00705B486C5AEB01E01E227CA01F>I< B712C0A216802203799427>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmr8 8 52 /Fx 52 127 df0 D<15F0A24A7E4A7EA24A7EA24A7E140E91381E7F80141C 91383C3FC014389138781FE014709138F00FF014E001016D7E14C001036D7E148001076D 7E1400010E6D7E824981163F4981161F498101F06E7E5B00016F7E5B00036F7E5B00076F 7E90C8FC486F7E120E001EEE7F80001FB8FC4817C0A24817E0A2B912F0342F7DAE3B>I< 140FA34A7EA34A7EA34A7EA3ECEFF014E7A2903801C7F814C301037F1483148101077F14 011400497F130E81011E80011C133FA2013C800138131FA20178800170130FA201F08049 1307A2000181491303A200038100071401D80FF0497ED8FFFC90387FFFF0A32C2F7EAE31 >3 D22 D<1307130F131E133C1378137013F0EA01E0120313C012 071380120F13005AA2121E123EA35AA612FC5AAD7E127CA67EA3121E121FA27E13801207 13C0120313E01201EA00F013701378133C131E130F130710437AB11B>40 D<126012F012787E7E120E120FEA078013C0120313E0120113F0120013F8A21378137CA3 133EA6133F131FAD133F133EA6137CA3137813F8A213F0120113E0120313C012071380EA 0F00120E121E5A5A5A126010437CB11B>I43 D<123C127E12FFA4127E123C08087A8714>46 D 48 D<130E131E137EEA01FE12FFA2EAFE7E1200B3AF13FF007F13FFA3182C7BAB23>III<140F5CA25C5CA25C5BA25BEB07BF143F130F13 1E131C1338137813F013E01201EA03C013801207EA0F00120E121E5A123812785AB612FC A3C7EA3F00A8EC7F8090381FFFFCA31E2D7EAC23>I<000CEB0180381F801F90B5FC1500 5C14F85C14C0D81C7CC7FC90C8FCA7EB1FC0EB7FF0381DFFFC381FE07EEB801F01001380 001EEB0FC0120CC7EA07E0A315F0A3123C127E12FEA215E0A248130F007014C00078EB1F 8000381400001E133E380F80FC6CB45A000113E038007F801C2D7DAB23>II<1238123E003FB512F8A34814F015E015C038700001EC0380EC 070048130EA25CC75A5CA25C495AA21303495AA2130F91C7FCA25BA25B133EA2137EA513 FEA8137C13381D2E7CAC23>III61 D65 DIIIIIIII75 DIIIII82 D<90383F80303901FFF07048EBFCF0380FC07E381F 000F001E1307481303007C1301127800F81300A21570A27EA26C1400127F7FEA3FF8EBFF 806C13F86C13FE6C7F6C14C0C614E0130F010013F0EC0FF814031401EC00FCA20060147C 12E0A46C1478A26C14F07E6CEB01E039FF8003C039F7F00F8000F1B5120038E07FFE38C0 0FF01E2F7CAD27>I<007FB712F8A39039800FE007D87E00140000781678A20070163800 F0163CA348161CA5C71500B3A74A7E011FB512F0A32E2D7EAC33>II<3B7FFFF007FFF8A3 0001D9800113006C90C712FC6D6C137016F06D6C485AD91FE05B15036D6C485AD907F890 C7FC903803FC0E151E6D6C5A903800FF3815786E5A6E5AA2141F6E7EA2814A7EEC1DFE14 3DEC78FF4A6C7E14E001016D7E49486C7E148001076D7E49486C7E010E6D7E5B013C6D7E 496D7EA2D801F8EC7F80D807FCECFFC0B5010713FFA3302D7EAC35>88 D91 D93 D98 D101 D I105 D<2607E07FEB0FE03BFFE1FFC03FF801E36D487E903AE783F0F07E3B 0FEE01F9C03F3B07F800FB001F03FF1480495BA2495BB2B53A1FFFE3FFFCA3361E7E9D3B >109 D<3903E03F8000FFEBFFE001E37F9038E781F8390FEE00FCEA07FC49137E5BA25B B2B5380FFFF0A3241E7F9D27>II<3803E07F39 FFE3FFE001E77F9038FF03F8390FFC00FC6C48137E497F491480151F16C0A2ED0FE0A816 C0151FA21680153F6DEB7F006D137E6D5B9038EF03F89038E7FFF001E313C0D9E07FC7FC 91C8FCA9B5FCA3232B7F9D27>I<13E0A41201A31203A21207120F121FB512F0A33807E0 00AE1438A70003137013F03801F8E0EA00FFEB7FC0EB1F00152A7FA81B>116 D<3AFFFE0FFF80A33A07F807F8000003EB03E0D801FC138000001307D97E0FC7FCEB7F1E EB3FBCEB1FB8EB0FF85C1307130380497E497EEB1E7EEB1C3F90383C1F8001787FEBF00F 48486C7E00036D7E390FF007F83AFFF80FFFC0A3221D7F9C25>120 D<38078010380FE03C381FF87C383FFFF84813F038F87FE038F01FC03820078016087AAC 23>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy msbm10 10.95 7 /Fy 7 91 df<007FB612FCB812C06C16F03B00E00781F3FC0170903800783E020EEB380F 93381C0780EF03C0EE0E01EF00E0A2821870A718E0A293380E01C01703EF078093381C0F 00EE3C1EEE787CEEF3F892380FFFE0020FB55A17F817FE913A0E007E3F8093380F07C093 380701E093380380F01878933801C03C181C180EEE00E0A21807A7180EA2933801C01C18 3C187893380380F093380781E093380F07C06E90381E3F8001E0903980FFFE00007FB712 F8B812C06C03F8C7FC383E7FBD29>66 D<007FB612F0B8FC6C16E03B01C007C07FF8D800 E09038001FFE020E9038079F8093380387C0933801C1F0717E0400133CEF701E180E717E 1980EF1C03F001C0A294380E00E0A31970A283A21938AC1970A3170EA219E0A3F001C017 1CF00380180705381300180EEF701E60EFF0784D5A933801C3E0933803C7C0DC079FC7FC 6EEB1FFED801C0903880FFF8007FB712E0B8C8FC6C15F03D3E7FBD2B>68 D<007FB512FCB6FC7E2601C00ECAFC6C6C5AB3B3A2F0018019C0F00380A31807A2180FF0 1F00606018F7EF03E7EF07C7EF1F076EECFE0ED801C0EC07F8007FB812FEB9FC7E3A3E7F BD33>76 D78 D<007FB612FCB812C06C16F83B01C007807F FED800E09039000F3F80020E90380707C093380381E0EF80F0933801C07884181C706C7E A284A8180EA34C485A183C604C485A93380787E093380F3FC093B5C7FC020FB512F817C0 04E7C8FC91390E1C0780ED1E0392380E01C003077F168003031370923801C078EEE03803 007FEE701EEE780EEE3807041C7FEE1E0393380E01C004077FEF80F004031370706C7EEF E03C04007FEF700F943878078094383803C048486C91381C01E0007FB500FE90381FFFFC B6806C823E3E7EBD39>82 D<903A01FF800180011FEBF003017FEBFE0F2601FF80B5FC39 07FC001FD80FB8EB07F3D81E70EB03C3D81CF0EB01E34848EB00F3167B0070153FD871C0 141F00E1150F1607EAE0E0A26D140313706D1401013E91C7FC7FEB07C0EB03F0EB00FC00 70EB3F800078EB0FE06CEB03FC6CEB007F6CEC1FC06C6CEB03E0D803E0EB00F86C6C147C D8007E141E6D6C7FD90FE0EB0780D901F8EB03C0D9007F130191391F8000E0EC07E0DA01 F81370EC007C031E13388100E0EC0780ED03C01501ED00E0A26C1570A37E6C1670A200EE 16E000EF1571D8E780ECE3C0D8E3C0ECE780D8E1E0903801CF00D8E7F8EB03FEB46C495A 9039FF803FF0D8F83FB512C0D8E00749C7FCD8600013E02D417DBF3A>I<0003B812F05A A2903B0FF8001C00E0D91F8090383801C0D80E7CC7EA78034902701380D80FE09138E007 005B49903801C00E90C70003131EEE801C001E4A485A1778001C020E1370031E5B151CC8 48485AED780303705B4B48C7FC5E913801C00E02035B15804A485A4A1378020E13704A5B A24A485AEC780302705B4A48C8FC01015BECC00E49485AA249485A491378010E01701406 4949140E140101385B9026780380141E13704948C8121C000149153CEBC00E484848157C 18FC48485A480178EC01DC000E017014034849EC079CD83C01ED1F1C003849EC3E384848 48EB01F8EE0FF0B912F8A3373E7DBD41>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmcsc10 10.95 29 /Fz 29 122 df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ndDVIPSBitmapFont %DVIPSBitmapFont: FA cmr10 10.95 84 /FA 84 128 df0 DI<153C157EA415FFA34A7FA34A7FA34A7FA215BFA291380F3FF0151FA2021E 7F150FA2023E7F143C1507027C7F14781503A202F07F81A20101814A7EA20103815C167F 0107815C163FA249C77F161FA24981011E140FA2013E81133C1607A249811603A201F881 000181487ED80FFF02071380B5D8F001B6FCA438417DC03F>3 D<010FB612F0A4D90001 0180C7FC6E90C8FCA8020713C091B512FE0107ECFFC0D91FFCEB7FF0D97FC0EB07FC49C6 EB01FED803FE913800FF80D807F8ED3FC0000F17E04848ED1FF049150F003F17F8007F17 FC491507A200FF17FEA6007F17FCA26D150F003F17F8001F17F06D151F6C6CED3FE00007 17C0D803FEEDFF80C66C913801FE00D97FC0EB07FCD91FFCEB7FF00107B612C001004AC7 FC020713C0020090C8FCA84A7F010FB612F0A4373E7BBD42>8 D<9239FF8007F0020F90 38E03FFC027F9038F8FFFE913AFF00FDFC3FD903F890387FF07F49489039FFE0FF809026 0FC0015BEB1F80013F5DD97F00ED7F006FEB003E017E6E90C7FC13FEADB97EA4C648C76C C8FCB3AC486C4A7E007FD9FC3FEBFF80A439407FBF35>11 DIII22 D<001E130F003FEB1F80397F803FC039FFC07FE0A301E013F0007F133F003F131F001EEB 0F7000001300A5484813E0A339038001C0A20007130301001380000EEB0700A248130E48 5B485B002013101C1C7DBE2D>34 D<121E123FEA7F80EAFFC0A313E0127F123F121E1200 A5EA01C0A3EA0380A212071300120EA25A5A5A12200B1C79BE19>39 D<1438147814F0EB01E0EB03C0EB0780EB0F00A2131E5B137C137813F85B1201485AA248 5AA3485AA3121F90C7FCA25AA2123EA2127EA5127C12FCB2127C127EA5123EA2123FA27E A27F120FA36C7EA36C7EA26C7E12007F1378137C133C7F7FA2EB0780EB03C0EB01E0EB00 F014781438155A78C323>I<12C07E7E12787E7E7EA26C7E6C7E7F12017F12007F137CA2 7FA37FA31480130FA214C0A21307A214E0A5130314F0B214E01307A514C0A2130FA21480 A2131F1400A3133EA35BA25B5B12015B12035B485A48C7FCA2121E5A5A5A5A5A145A7AC3 23>I<1506150FB3A9007FB912E0BA12F0A26C18E0C8000FC9FCB3A915063C3C7BB447> 43 D<121E123FEA7F80EAFFC0A313E0127F123F121E1200A5EA01C0A3EA0380A2120713 00120EA25A5A5A12200B1C798919>II<121E123FEA7F80EAFFC0 A4EA7F80EA3F00121E0A0A798919>III<14E013011303130F 137FEA07FFB5FCA2139FEAF81F1200B3B3AA497EB612FCA41E3D78BC2D>III<151E153EA2157E15FEA21401A2 14031407A2140E141E141C143C1478147014F0EB01E014C01303EB078014005B131E131C 133C5B137013F05B485A12035B48C7FC5A120E121E5A123812785AB8FCA4C73801FE00AB 4A7E0103B6FCA4283E7EBD2D>I<00041403D80F80131F01F813FF90B55A5D5D5D15C05D 4AC7FCEB7FF090C9FCACEB01FE90380FFF804913E090387E07F09038F001F8496C7E4913 7E49137F90C7EA3F801206C813C0151F16E0A316F0A4123E127F487E7FA216E05B90C7FC 007EEC3FC0127016806C147F003C15006C14FE6C495A9038C003F83907F00FF00001B55A 6C1480D93FFEC7FCEB0FF0243F7CBC2D>II<1238123C123F90B612FCA44815F816F0A216E00078C7EA03C00070EC0780 A2ED0F00151E5A5D5DA2C85A4A5A4A5AA24A5A140F92C7FC5C141E143E143C147CA25CA2 1301A2495AA31307A3130F5CA3131FA5133FA96D5AA20107C8FC26407BBD2D>III<121E 123FEA7F80EAFFC0A4EA7F80EA3F00121EC7FCB3121E123FEA7F80EAFFC0A4EA7F80EA3F 00121E0A2779A619>I<121E123FEA7F80EAFFC0A4EA7F80EA3F00121EC7FCB3121E123F EA7F8012FF13C0A3127F123F121F1201A5EA0380A4EA0700A2120EA25AA25A5A12200A39 79A619>I<007FB912E0BA12F0A26C18E0CDFCAE007FB912E0BA12F0A26C18E03C167BA1 47>61 D65 DIIIII< DB3FE0130C912603FFFC131C021F01FF133C027F14C0913AFFF00FE07C010390390001F0 FCD907FCEB0079D90FF0143D4948141F4948140F4948140749C81203485A484815011207 491500120F5B001F177CA2485AA2183C127FA25B95C7FC12FFAB043FB512F0127FA27F93 39000FFE00003F705AA27F121FA26C7EA212077F6C7E12016C7E6D7E6D6C140F6D7ED90F F8141FD907FE143E6D6C6CEBFC7C01009039F007F83C6EB5EAE01C021FECC00C020349C8 FC9138003FF03C427BBF47>III75 DIIIII82 DI<003FB91280A4D9F000EBE001018090397FC0003F48C7ED1F C0007C1707A200781703A300701701A548EF00E0A5C81600B3B04B7E010FB612FEA43B3D 7DBC42>IIII<003FB7 12F8A317F091C7123F01F815E001E0147F0180ECFFC090C81380003E5C1700484A5A1507 00785D150F4B5A5E0070143F5E4B5A15FF5EC75A4A90C7FC5D14075D4A5A141F5D143F4A 5A5D14FF5D4990C8FC5B4A141C1307495A5C131F5C495A017F153C5C13FF485B91C8FC48 16785B484815F8120F491401001F15034848140F49143F007FEC01FF90B7FCB8FCA32E3E 7BBD38>90 DI<6D1340486C13E0 39038001C03907000380000EEB0700A248130E003C131E0038131CA2485BA3485BA500EF EB778039FF807FC001C013E001E013F0007F133FA3393FC01FE0391F800FC0390F000780 1C1C73BE2D>II97 DI<49B4FC010F13F001 3F13FC90387F007E01FC7F48485B4848EBFF80485A120F485AED7F004848133E151C007F 91C7FCA290C9FCA25AA97E7FA2123FED01C06C7EED03806C7E0007EC07007F6C6C130ED8 01FE133C39007F80F86DB45A010F13C0D901FEC7FC222A7DA828>IIII<167C903903F803FE90391FFF07FF017F9038DF 9F809039FE0FFE1F3901F803F82603F001EB0F003A07E000FC0693C7FC4848137EA2001F 147FA7000F147EA26C6C5BA26C6C485A6C6C485A3903FE0FE090B55AD8071F90C8FCEB03 F848CAFCA57F7F6CB512F015FE6C6E7E6C15E0488148813A0FC0001FFC48C7120348EC00 FE007E157E167F4881A5007E157EA26C5D6C6C495A6C6C495AD807F0EB0FE0D803FEEB7F C0C6B6C7FC013F13FC010313C0293D7EA82D>III<147814FCEB01FE EB03FFA4EB01FEEB00FC14781400AC147FEB7FFFA413017F147FB3B3A4123E127F38FF80 7E14FE14FCA2EB01F8007E13F0383E07E0381FFFC06C1300EA01FC185185BD1C>III<2701F801FE14FF00FF90270FFFC0 0713E0023FD9E01F7F913B7C07F03E03F8913BF003F87801FC3D07F9C001FCE000FE2603 FB80EBFDC000010200157E01FFC7B448137F4992C7FCA3495CB3A5486C496CECFF80B5D8 F87FD9FC3F13FEA447287DA74C>I<3901F801FE00FF90380FFFC0023F7F91387C07F091 38F003F83A07F9C001FC3803FB800001140001FFC77E5BA35BB3A5486C497EB5D8F87F13 FCA42E287DA733>I<14FF010713E0011F13F890387F81FE9038FC003F4848EB1F804848 EB0FC04848EB07E04848EB03F0001F15F8491301003F15FCA248C812FEA44815FFA96C15 FEA36C6CEB01FCA36C6CEB03F8000F15F06D13076C6CEB0FE06C6CEB1FC06C6CEB3F803A 007F81FE006DB45A010F13F0010090C7FC282A7EA82D>I<3901FC03FC00FF90381FFF80 4A13E09138FC0FF89039FDE003FC3A07FF8000FE6C90C7127F6C481580163F49EC1FC017 E0A2160F17F0A2160717F8A917F0160FA217E0161F17C0163F6D1580EE7F006D14FE6E48 5A9039FDE003F89039FCF80FF091387FFFC0021F5BDA03FCC7FC91C9FCAC487EB512F8A4 2D3A7EA733>I<02FE131C903907FFC03C011F13E090387F80F09039FE00387C4848131C 4848EB0EFC4848130748481303121F5B003F14015B127FA290C7FC5AA97E7FA2123F7FA2 001F14036C7E6C6C1307150F6C6C131DD801FE137939007F81F190383FFFE1010F138190 3801FC0190C7FCAC4B7E92B512F8A42D3A7DA730>I<3901F80FC000FFEB3FF0EC7FF8EC F1FC9038F9C3FE3807FB8312033801FF03EC01FC9038FE00F815701500A25BB3A4487EB5 12FEA41F287EA724>I<90383FC0603901FFF8E0000713FD380FC03F381E000F48130312 7C0078130112F81400A37E7E6C6C1300EA7FF0EBFF806C13F86C7F6C13FF6C1480000114 C06C6C13E013039038003FF014070060EB03F800E01301A26C1300A37E15F06C130115E0 6C130339FF8007C039FBE01F8000F1B5120000E013FC38C01FE01D2A7DA824>I<131CA6 133CA4137CA213FCA2120112031207001FB512C0B6FCA3D801FCC7FCB315E0A90000EB01 C013FE137E90387F038090383F8700EB1FFE6D5AEB01F81B397EB723>IIIIII<001FB6 1280A3D9E000130001805B49485A001E1303001C495A003C5C140F4A5A0038495A5D147F 4AC7FC5CEA0001495A495A5C130F90391FE00380EB3FC01480137FEBFF005B0001140748 5A485A491400000F5C485A495B4848137F007F495AB7FCA321277EA628>I126 D<001C130E007EEB1F80007F133F39FF807FC0A3397F003F80007E 131F001CEB0E001A0977BD2D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB msam9 9 1 /FB 1 63 df<126012F812FEEA7F80EA1FE0EA07F8EA01FE38007F80EB1FE0EB07F8EB01 FE9038007FC0EC1FF0EC07FCEC01FF9138003FC0ED0FF0ED03FCED00FFEE3FC0EE0FF0EE 03FCEE00FEA2EE03FCEE0FF0EE3FC0EEFF00ED03FCED0FF0ED3FC003FFC7FCEC07FCEC1F F0EC7FC04948C8FCEB07F8D91FE0140CD97F80143ED801FEC812FED807F8EC03FCD81FE0 EC0FF0D87F80EC3FC000FEC8EAFF0000F8EC03FC0060EC0FF0C8EA3FC003FFC7FCEC07FC EC1FF0EC7FC04948C8FCEB07F8EB1FE0EB7F80D801FEC9FCEA07F8EA1FE0EA7F8000FECA FC12F812602F3E7AB03C>62 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmmi9 9 12 /FC 12 127 df13 D<143CECFFE04913FC4913FEEB07031400010E137C15181500130FA28013 0780A26D7E80130180806D7E801303010F1380EB1FBF90387E3FC0EBF81FD801F013E038 03E00F120713C0380F8007121F13005AA2127EA4007C14C012FC140F1580A2007C131F15 00141E6C133E143C6C5B6C6C5A6CB45A6C5BC690C7FC13081F387EB522>I<121C127E12 7FEAFF80A213C0127FA2121D1201A4EA0380A3EA0700A2120EA25A5A5A12200A187A8815 >59 D<0107B612F04915FEEFFF80903B001FC0003FE0EF0FF04A48130718F8170318FC4A C7FCA402FE15F8170718F0170F494815E0EF1FC0EF3F80EFFF004948EB03FEEE0FF891B6 12E05F4915F09139F00007FCEE01FE707E4948801880173F18C0495AA449481580177FA2 EFFF0049C8FC4C5A4C5A4C5A01FE4A5AEE3FE00001913801FF80007FB648C7FCB712F816 C036337DB23A>66 D<010FB67E17F817FE903A001FC001FF9338003FC04A48EB1FE0170F EF07F0A24AC7FC18F8A302FEEC0FF0A3EF1FE0494815C0173F1880EF7F004948EB01FEEE 03F8EE3FE091B61280494AC7FC5E9138F0007F707E4948131F707E83A2495AA44948131F A35F49C7123FA2180C180E01FE161CA20001031F1338B500FCECE070040F13F04A903807 FFE0C96C13809338007F0037357DB23A>82 D<0007B812C05AA2903AF000FE003FD81F80 150749485A001EEE03805AA20038495AA248160718004A5A5AA34849481306C792C7FCA3 4A5AA44A5AA44AC9FCA414FEA4495AA4495AA4495AA2130F001FB512F848805D32337EB2 2D>84 D<267FFFFE90381FFFF8A24A15F0C648C81300177C484815781770A348485DA448 484A5AA448484A5AA448484AC7FCA44848140EA448C85AA400FE5DA35EA25A5EA24B5A4B 5A007E4AC8FCA2003E141E003F5C6C14F0390FC003E03907F01FC06CB5C9FCC613FCEB1F E035357BB234>I100 D104 D110 D<01F0130ED803FC131F486CEB3F80D80F1F137F121C153F0038EB801FEC000F485AA201 7E130700E015001260C65AA2150E485AA25D485AA25DA2153015705DA24A5A4A5A3801F8 072600FC1FC7FCEB7FFEEB3FF8EB07E021227EA025>118 D<156015F0A21578A2157C00 7FB6FCB7FCA27EC812FCEC01F0EC03E0EC07C01580EC0300201072B526>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FD cmcsc10 9 46 /FD 46 119 df<127812FCA27E7EEA7F80EA1FC0EA0FE0EA07F01203EA00F8137C133C13 1C0E0E77B329>18 D<137813FCA212011203EA07F8EA0FE0EA1FC0EA3F801300127C5A5A 5A0E0E6FB329>I<123C127FEAFF80A313C0A2127F123E1200A4EA0180A3EA0300A21206 120E120C5A5A12200A18798818>44 DI<121C127FA2EAFF80A3 EA7F00A2121C0909798818>I48 D<13075B133F13FF120FB5FC133F12F01200B3B3A2497EB612C0A31A3278 B129>IIII<00181460391F8007E090B512C01580150014FC14F014C0001C C8FCAAEB0FE0EB3FF8EBF03E381DC00F391F000780001E14C0EC03E0001C14F01208C7EA 01F8A315FCA4123C127EB4FCA315F85A481303007014F0A26CEB07E0003C14C06CEB0F80 6CEB1F003807C0FE6CB45A6C13F038003F801E347BB129>I<14FF010313C0010F13E090 383F81F090387E007801F813F83901F001FC3803E003EA07C0A2EA0F80001FEB01F890C7 12F015005AA2127EA2EB07FCEB1F7F39FE38078090386003E0EBC001EC00F06C4813F815 FC90C7127C157EA25A157FA4127EA5003E147E123FA26C14FCA26C6C13F80007EB01F001 C013E03803E0073901F81F806CB51200EB3FFEEB0FF020347CB129>I<1238123E003FB6 1280A34815005D5D0078C7121C00705C5D5D5A4A5A4A5AC7FC4AC7FC140E5CA25C147814 7014F05C13011303A2495AA3130FA2131F5CA3133FA5137FA86DC8FC131E21347BB129> I57 D<15F0A34A7EA24A7EA34A7EA34A7EEC0E7FA24A6C7EA34A6C7EA202787FEC700F A202F07FECE007A2010180ECC003A249486C7EA349C77EA349B6FCA24981011CC7123FA2 013C810138141FA24981160FA2496E7EA300016F7E487ED80FF84A7EB591B512F0A33436 7CB53D>65 D67 D70 D73 D<013FB51280A39039001FF0006E5AB3B0121C127FA2EAFF80A25DEB00 1F7E007C5C003849C7FC0018133E000E5B380781F83803FFE0C66CC8FC21357CB22A>I< B6FCA3000190C9FC6C5AB3A917E0A4160117C0A41603A21607160F161F163FEE7F800001 EC03FFB8FCA32B337DB233>76 D II80 D82 D<90391FF00180EB7FFE48B512833903F00FC73907C003E748C712FF001E147F48143F15 1F48140FA200F81407A315037EA27E007E91C7FCEA7F807FEA3FF8EBFF806C13F86CEBFF 806C14E06C14F8C680013F7F01037FEB003F02031380EC007FED3FC0151FED0FE0150712 E01503A47E16C07E15076C15806C140F6C15006D131ED8F3E0137C39F1FE01F839E07FFF F0D8C01F13C0D903FEC7FC23377BB42E>I85 DI<143CA2147EA314FFA3903801DF80A201037F148FA20107 7F1407A290380E03F0A2011E7FEB1C01A2013C7FEB3800A249137E90387FFFFE90B6FCA2 9038E0003F0001158049131FA24848EB0FC0A2486C14E0EA1FE0D8FFF890B5FCA328277E A62E>97 DI<02FF1330010713E0011FEBF07090397FC07CF090 38FE001FD801F8130748481303485A48481301485A150048C8FCA2481570127EA200FE15 00A8127E1670127F7EA26C6C14E0A26C6C13016C6C14C06C6CEB03806C6C1307D800FEEB 0F0090387FC07C90381FFFF8010713E00100138024287DA62C>III<02FF13 30010713E0011FEBF07090397FC07CF09038FE001FD801F8130748481303485A48481301 485A150048C8FCA2481570127EA200FE1500A64AB5FCA2127E91380007F0007F14037EA2 6C7EA26C7E6C7E6C7E6C6C1307D800FE130F90387FC03E90391FFFFC700107EBF0100100 EB800028287DA630>103 DII108 DII<49B4 FC010F13E090383F01F890387C007C4848133FD803E0EB0F80000715C04848EB07E04913 03001F15F048C7EA01F8A24815FCA2007E1400A200FE15FEA9007FEC01FCA36C15F86D13 03001F15F06D1307000F15E06C6CEB0FC06C6CEB1F806C6CEB3F006C6C137E90383F01F8 90380FFFE0010190C7FC27287DA62F>II<49B4FC010F13E090383F01F890387C007C4848133F4848EB1F804848EB0FC04848 EB07E0491303001F15F0003F15F890C712014815FCA2007E1400A200FE15FEA9007E15FC 007F1401A26C15F8A23A1F807C03F014FE3A0FC18307E03A07E3018FC0D803F3EB9F803A 01FB00FF006CB45B90383F81F890390FFFE0060101137090C7FCED780EED7C1EED7FFC15 3FA216F8ED1FF0ED0FE0ED07C027327DA62F>III<007FB612F8A3903800FC03007C1400007815780070153800F0153CA24815 1CA5C71400B3A2497E90387FFFF8A326267EA52C>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: FE cmr9 9 76 /FE 76 124 df0 D<91391FE007F09139FFF81FF801079038FE7FFC903A0F E01FFC7E903A1F803FF0FF90397E007FE0495C5B0001167E4990383F803C0003021F1300 ABB812C0A33B03F0001F8000B3A7486C497EB50083B5FCA330357FB42D>11 DI<127812FCA27E7EEA7F80EA1FC0120FEA07E0EA03F0EA01F8 1200133C13180E0E78B326>18 D<137813FCA212011203EA07F8EA0FE013C0EA1F80EA3F 00127E127C12F012600E0E71B326>I40 D<12C07E7E12787E7E120E120F6C7E6C7EA26C7EA26C7EA27F1378 137CA2133C133EA3131E131FA51480A2130FAC131FA21400A5131E133EA3133C137CA213 7813F85BA2485AA2485AA2485A48C7FC120E121E5A5A5A5A5A114A7BB71E>I<156015F0 B3A4007FB812C0B912E0A26C17C0C800F0C8FCB3A4156033327CAB3C>43 D<121C127E127FEAFF80A213C0127FA2121D1201A4EA0380A3EA0700A2120EA25A5A5A12 200A187A8815>II<121C123E127FEAFF80A3EA7F00123E121C09 097A8815>I48 D<13075B5B13FF120FB5FC133F12F01200B3B3A2497E007FB51280A319327AB126>IIII<000814C0381F800F90B5FC1580ECFE005C14F014C0D81C7CC7FC90C8FCA9EB0FC0EB 3FF8EBFFFC381DF07E381FC01F9038000F8015C0001E1307001C14E0000C14F0C71203A3 15F8A31218123E127F5AA215F0A2481307007814E012700078EB0FC0003814806CEB1F00 6C133E3807C0FC6CB45A6C13E038007F801D347CB126>I<14FE903807FF804913C09038 3F01E090387C00709038F801F03901F003F83803E007EA07C0A2EA0F80001FEB03F0EC01 E048C8FCA35A007E7FEB07F8EB1FFE38FE3FFF9038700F809038E007C09038C003E039FF 8001F015F81300EC00FCA25A15FEA4127EA56C14FCA36CEB01F8A2D80F8013F0EC03E0EA 07C03903E007C03901F81F803900FFFE00EB3FFCEB0FE01F347DB126>I<1238123E003F B6FCA34814FE15FCA20078C712380070147015E0A248EB01C0EC0380A2C7EA0700140E5C A25C5CA25C1301A2495AA213075C130FA2131FA349C7FCA35BA55BA8137E133C20347CB1 26>III<121C123E127F EAFF80A3EA7F00123E121CC7FCAE121C123E127FEAFF80A3EA7F00123E121C09207A9F15 >I<121C123E127FEAFF80A3EA7F00123E121CC7FCAE121C127E127F5A1380A2127FA212 1F1203A4EA0700A4120EA25A123C12385A1220092F7A9F15>I<007FB812C0B912E0A26C 17C0CCFCAC007FB812C0B912E0A26C17C033147C9C3C>61 D<15E04A7EA34A7EA34A7EA3 EC0EFEA3EC1C7FA34A6C7EA202787FEC701FA202F07FECE00FA2010180ECC007A2010380 EC8003A249486C7EA3010E6D7E010FB5FCA24980011CC77EA2496E7EA20178810170141F A201F08149140FA20001821607487ED80FF84A7EB549B512E0A333367DB53A>65 DIIIIIIII<013FB51280A39039001FF0006E5AB3B012 1C127FA2EAFF80A25DEB001F7E007C495A003891C7FC6C137E380F81FC6CB45A6C13E0C6 6CC8FC21357EB227>II IIIII82 D<90381FE00390387FFC0748B5FC3903F01F8F39078003DF48C7B4FC001E8048 80A24880A200F880A381A27EA2007E91C7FC127F13C0EA3FF013FF6C13F06C13FF6C14C0 6C80C614F8013F7F01037FEB003FEC03FF1400ED3F80151F16C0150F126000E01407A47E 1680A26C140F16006C5C6C141E6C6C5BD8FBE013F839F1FC03F000E0B55A011F138026C0 03FEC7FC22377CB42B>I<007FB712FEA39039C007F001D87E00EC007E007C163E007816 1E170E127000F0160FA3481607A6C71500B3AB4A7E011FB512FCA330337DB237>IIII89 D<003FB612FCA39039FC0003F801E0EB07F00180130F90C713E0003EEC1FC0003C143F00 7C15800078EC7F005D5D007013014A5A5D14074A5AC75B141F5D4A5A147F92C7FC14FE13 015C495A13075C495A011F141C5C133F495A91C7FC5B4848143C5B12035B48481478120F 4914F848481301003F140349130F48C7127FB7FCA326337CB22F>II93 D97 DII<153FEC0FFFA3EC007F81AEEB0FF0EB7FFC 90B5FC3901FC0FBF3907E001FF48487E497F001F8048C7FCA25A127EA212FEA8127EA212 7F7EA26C6C5B5D6C6C5A6C6C4813803A03F81F3FFC3801FFFE38007FF8D91FE013002635 7DB32B>II<14FEEB03FF010F 138090381F8FC090383E1FE0137C13F81201EC0FC03903F0078091C7FCABB512F0A3D803 F0C7FCB3A7487E387FFFE0A31B357FB417>I<151F90391FC07F8090387FF0FF3A01FFFD E7C03903F07F873907C01F073A0F800F8380001FECC000EB00074880A76C5CEB800F000F 5C6C6C48C7FCEBF07EEBFFFC380C7FF0EB1FC0001CC9FCA2121EA27EEBFFFE6CEBFFC015 F06C80000F80391F0001FE003EEB007F48141F168048140FA5007CEC1F00A2003F147E6C 6C5B390FF007F80003B512E0C61480D91FFCC7FC22337EA126>II<1207EA0F80EA1FC0EA3FE0A3EA1FC0EA0F80EA0700C7FC A9EA07E012FFA3120F1207B3A6EA0FF0B5FCA310337EB215>I107 DI<2703F01FE013 FF00FF90267FF80313C04A6C487F903BF3C0FE1E07F03C07F7003F3801F8D803F6143001 FC90391FE000FC495CA3495CB3486C496C487EB53BC7FFFE3FFFF0A33C217EA041>I<39 03F01FC000FFEB7FF09038F1FFF89038F3C0FC3907F7007EEA03FE497F5BA35BB3486CEB 7F80B538C7FFFCA326217EA02B>II<3903F03FC000FFEBFFF001F313FC9038F7C0FE3907FE007F6C48EB3F8049 EB1FC049130F16E0150716F0A2150316F8A816F01507A216E0150F6D14C0ED1F806DEB3F 006D137E9038F781FC9038F3FFF801F113E09038F03F8091C8FCAA487EB512C0A325307E A02B>I<90380FE00790383FFC0FEBFFFE3801FC0F3903F0039F3907E001DF48486CB4FC 48487F123F90C77E5AA2127E12FEA8127E127FA27E6D5B121F6D5B6C6C5A3907F007BF39 03F81F3F3800FFFEEB7FF8EB0FE090C7FCAAED7F8091380FFFFCA326307DA029>I<3803 E07C00FF13FF01E113809038E39FC03807E71FEA03EE9038EC0F809038FC070049C7FCA3 5BB2487EB512E0A31A217FA01E>II<1370A513F0A31201A212031207120F121FB512FEA33803F000AF14 07A8140EEA01F8A23800FC1CEB7FF8EB3FF0EB0FC0182F7FAD1E>III II<3A7FFF80FFF8A33A07F8003FC06C48EB1F806C6CEB0F00150E6D131E0000141C A2017E5BA2017F13786D1370A26D6C5AA214C1010F5B14E301075BA2D903F7C7FCA214FF 6D5AA26D5AA31478A21470A214F05CA2495A127CEAFE035C49C8FC5BEAFC1EEA783CEA3F F86C5AEA07C025307F9F29>I<003FB512F0A39038800FE0393E001FC0003C1480003813 3F0078EB7F0014FE00705B1301495A495A00005B495A131F495AEC0070137E13FE485A48 5A4913F01207484813E0381FC0011380003F1303387F001FB6FCA31C207E9F22>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: FF cmbx10 10.95 50 /FF 50 122 df12 D40 D<127012F8127C7E123FEA1FC06C7E12076C7E7F6C7E6C7EA2137F80 133F80131F80130F80A26D7EA3801303A280A36D7EA61580B01500A6495AA35CA213075C A3495AA25C131F5C133F5C137F91C7FC13FEA2485A485A5B485A120F485A48C8FC123E5A 5A1270195A7AC329>I46 D<140F5C147F495A130F48B5FCB6FCA313F7EAFE071200B3B3 A8003FB612F8A5253C79BB34>49 D<903803FF80013F13F090B512FE00036E7E4881260F F80F7F261FC0017F003F6D7FD87FF06D7E6D6D7EA2486C6D7EA36F1380A26C5AA26C5A6C 5A0003C7FCC8481300A35E153F5E4B5AA24B5A4A5B5E4A90C7FC4A5A4A5A4A5A15E04A5A 4A5A9139FE000F80495A495A4948EB1F00495AEB1F8049C7FC017E5C5B48B7FC485D5A5A 5A5A5AA2B75AA4293C7BBB34>III<000E1538D8 0FC0EB01F801FC131F90B6FC5E5E5E5E93C7FC5D5D15F015C092C8FC14F801C0C9FCA8EC FFC001C713F801DF13FE90B67E02017F9039F8007FF001E08049133F498090C76C7EC8FC 82A31780A21207EA1FC0487E487E487EA31700A25B007F5D49133F01805C6CC7485A7F3A 1FE001FFF0260FF8075B6CB612806C92C7FCC614FC013F13E0D907FEC8FC293D7BBB34> I<16FC4B7EA24B7EA34B7FA24B7FA34B7FA24B7FA34B7FA292B57E15FD15FC020180EDF8 7F02038015F0820207814B7E020F8115C082021F814B7E023F811500824A81027E7F02FE 815C8201018291B7FC4982A3498302E0C7121F010F835C83011F834A80013F8391C8FC83 4983017E81B500FE49B612FCA5463F7CBE4F>65 D<922607FF80130E92B500F8133E0207 02FE137E021F9138FF80FE027F15E149B538801FFB01079039F80003FF4901C07F013F90 C8127F4948153F4948151F4849150F4A150748491503485B1801485B481700A291CAFC5A 197E5A5BA2190012FFAC127FA26D173EA27EA27E80197C7E6C7F19F86C6D15016C6D16F0 6E15036C6DED07E06D6CED0FC06D6CED3F80010F01C0EC7F006D01F8EB01FE01019039FF 801FFC6D6C90B512F0021F15C0020792C7FC020014FC030713C03F407ABE4C>67 DIII<922607FF80130E92B500F8133E020702FE137E021F9138 FF80FE027F15E149B538801FFB01079039F80003FF4901C07F013F90C8127F4948153F49 48151F4849150F4A150748491503485B1801485B481700A291CAFC5A197E5A5BA296C7FC 12FFAB040FB612FC127FA27FA26C92C7387FFE00A27E80A27E6C7FA26C7F6C7F806C7F6D 7E6D6C6C14FF010F6D5B6D01F85B01019038FF801F6D6C90B512F3021F15C00207ED003E 020002FC130E030701C090C7FC46407ABE52>III75 DIIIII82 D<903A01FF8001C0011FEBF807017FEBFE0F90B6129F000315FF48EB007FD80FFC130FD8 1FF01303497F003FEC007F5B007F153F161FA200FF150FA36D1407A27F7F01FE91C7FCEB FFE06C13FEECFFF06C14FF16C06C15F0826C816C816C816C16806C16C0133F010F15E013 01D9001F14F01400150F030113F881167F0078153F12F8A2161FA36C16F0A27E17E06C15 3F6D15C06D147F01F0ECFF8001FE4913009038FFE00791B512FCD8FE3F5CD8FC0F14E0D8 F803148027E0001FFCC7FC2D407ABE3A>I<003FB912FCA5903BFE007FFE007FD87FF0EE 0FFE01C0160349160190C71500007E187EA3007C183EA400FC183F48181FA5C81600B3AF 011FB712F8A5403D7CBC49>II<007FB6D8807FB512F0 A5D8001F01E0C76CC7FC6D5E6F495A6D6D5C6D6D495A17076D6D495A6D6D5C6E4A5AEE80 3F6E01C05B6E4AC8FCEEE0FE6E13F16EEBF9FCEEFBF86E13FF6E5C6E5C5F816F5B836F7F 6F7FA26F7F835D834B7F5D4B80043F7FDBFE1F7F14014A486C7F4B6C7F4A487E020F814B 6C7F4A487E4A4880027F6E7F92C76C7F14FE01016F7F49486E7F4A80494882010F6F7F49 4880B600E090B7FCA5483E7DBD4F>88 D<903803FF80013F13F890B512FE00036E7E2607 FC017F48486C6C7E6D6D7E001F816D131F82150F826C5AA26C5AEA01E0C8FC153FEC7FFF 0107B5FC133F9038FFFC0F000313E0000F1300485A485A5B485AA2485AA4151FA26C6C13 3F6DEB7BFF6C6C01F313FE391FFE03F16CB512E10003EC807FC69038FE001FD90FF890C7 FC2F2B7DA933>97 D<13FFB5FCA512077EAFED7FE0913807FFFC021F13FF027F14C04AC6 7F02FCEB3FF802F06D7E4A6D7E4A13074A6D7EA21880A27013C0A318E0AA18C0A34C1380 A218005E6E5C6E495A6E495A6E495A903AFCFF01FFE0D9F83FB51280496C91C7FCD9E007 13F8C813C033407DBE3A>IIIII<903A03FF80 07E0011F9038F03FF8017F9038FCFFFC48B712FE48010113F13A07FC007FC14848EB3FE1 17FC484890381FF0F81700003F81A7001F5DA26C6C495AA26C6C495A6CB448485A91B5C7 FC4814FC019F13F0D80F03138090CAFCA27F121F7F6C7E90B512FEEDFFE016FC6C81EEFF 806C16C07E000716E0001F16F0393FE0000149EB003F4848EC0FF890C8FC481507A56C6C EC0FF0A26C6CEC1FE0D81FF0EC7FC06D14FF2707FF800F13006C90B55AC615F8011F14C0 010101FCC7FC2F3D7DA834>I<13FFB5FCA512077EAFED1FF0EDFFFE02036D7E4A80DA0F C07F91381F007F023C804A133F5C4A80A25CA25CB3A5B5D8FE0FB512E0A5333F7CBE3A> II<13FFB5FCA512077EB092380FFFFEA5DB01FEC7FC4B 5AED07F0ED1FE04B5A4B5A03FEC8FC4A5AEC07F84A5A141F4A7E14FF8181ECF7FF02E77F 14C302817F02007F6F7E82153F6F7E6F7E6F7E83816F7F6F7FB5D8FC07EBFFC0A5323F7D BE37>107 D<13FFB5FCA512077EB3B3AFB512FCA5163F7CBE1D>I<01FFD91FF8ECFFC0B5 D97FFF010313F84AB5D8C00F13FE0207DAE03F7F91290FE07FF07F037F91261F003FEBF8 010007013CDAF9E0806C4990391FFBC00002705D4A02FFC77FA24A5CA24A5CB3A5B5D8FE 07B5D8F03FEBFF80A551297CA858>I<01FFEB1FF0B5EBFFFE02036D7E4A80DA0FC07F91 381F007F0007013C806C49133F5C4A80A25CA25CB3A5B5D8FE0FB512E0A533297CA83A> II<01FFEB7FE0B53807FFFC021F13 FF027F14C0DAFF017F9139FC007FF8000701F06D7E6C496D7E4A130F4A6D7EA2701380A2 18C0A28218E0AA18C05EA218805E1800A26E495A6E495A6E495A6E495A9139FF01FFE002 BFB51280029F91C7FC028713F8028013C092C9FCACB512FEA5333B7DA83A>II<3901FE01FC00FFEB0FFF4A13C04A13E091387E 3FF0147800079038F07FF8000313E013FF14C0ED3FF01480ED1FE0ED078092C7FC91C8FC B3A3B6FCA525297DA82B>I<90381FFC0E90B5123E000314FE120F381FE007383F800190 C7FC007E147E153E12FEA27EA201C090C7FC13F8EBFFE06C13FE6E7E6C14E06C14F86C80 6C800001806C7E010F1480EB007F020313C014000078147F00F8143F151F7EA26C1580A2 6C143F6D14006D137E9038F803FE90B512F8485CD8F83F13C026E00FFEC7FC222B7DA929 >III 119 D121 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 478 632 a FF(PHASE)45 b(COEXISTENCE)e(F)m(OR)i(THE)f(KA)m(C)h (ISING)g(MODELS)1627 881 y FE(T.)26 b(BODINEA)n(U)417 1312 y FD(Abstra)n(ct.)42 b FE(W)-6 b(e)35 b(deriv)n(e)g(the)f(W)-6 b(ul\013)35 b(construction)g(for)h(Kac)f(Ising)g(mo)r(dels)g(with)g (long)h(but)e(\014-)417 1404 y(nite)29 b(range)g(in)n(teraction)h(in)f (dimensions)f FC(d)f FB(>)f FE(2.)45 b(Some)28 b(op)r(en)h(problems)f (concerning)i(the)e(phase)417 1495 y(co)r(existence)f(for)f(more)f (general)i(mo)r(dels)f(are)g(also)h(discussed.)1523 1732 y FA(1.)46 b Fz(Intr)n(oduction)218 1894 y FA(During)19 b(the)j(last)f(decade)g(imp)s(ortan)m(t)f(progress)h(has)g(b)s(een)f (made)h(in)f(the)h(thorough)g(understanding)118 2002 y(of)40 b(the)f(phase)g(co)s(existence)h(phenomenon.)67 b(The)39 b(most)g(precise)g(quan)m(ti\014cation)g(of)g(the)h (di\013eren)m(t)118 2110 y(mec)m(hanisms)35 b(at)h(pla)m(y)g(and)f(a)h (sharp)e(description)g(of)i(the)g(phase)f(b)s(oundaries)f(has)h(b)s (een)g(obtained)118 2217 y(in)d(the)h(con)m(text)h(of)f(the)g(2D)h (Ising)e(mo)s(del)g(with)f(nearest)i(neigh)m(b)s(or)f(in)m(teractions)h ([DKS)o(,)h(Pf)o(,)f(A)m(CC,)118 2325 y(I1,)k(I2)q(,)g(DS,)g(ScS1)o(,)g (ISc,)g(PV1)q(,)g(PV2,)g(DH)q(,)g(Al)o(].)60 b(F)-8 b(or)38 b(the)f(3D)g(Ising)f(mo)s(del,)h(the)g(results)f(are)h(less)118 2433 y(precise)h(and)g(the)g(phase)g(segregation)h(is)f(c)m (haracterized)h(b)m(y)g(the)f(concen)m(tration)h(in)e Fy(L)3223 2400 y Fx(1)3307 2433 y FA(of)h(coarse)118 2541 y(grained)31 b(con\014gurations)h(to)g(the)h(equilibrium)27 b(crystal)32 b(shap)s(es)f([ABCP,)i(BCP,)f(BBBP)q(,)g(BBP)q(,)g(Ce,)118 2649 y(B1)q(,)f(CePi1,)g(CePi2,)g(BIV2)q(].)44 b(F)-8 b(or)32 b(a)f(comprehensiv)m(e)g(surv)m(ey)g(on)g(the)g(topic)g(the)h (reader)f(is)f(referred)118 2757 y(to)h([BIV1)q(])g(and)f(the)g (references)h(therein.)218 2865 y(In)39 b(this)g(pap)s(er)g(a)i (di\013eren)m(t)e(approac)m(h)h(is)g(implemen)m(ted)e(in)h(order)g(to)i (obtain)f(the)g(W)-8 b(ul\013)40 b(con-)118 2973 y(struction)32 b(for)h(Kac)g(Ising)f(mo)s(del)g(with)f(\014nite)h(range)h(in)m (teractions.)48 b(The)33 b(motiv)-5 b(ation)32 b(b)s(ehind)e(this)118 3081 y(strategy)c(is)e(to)i(pro)m(vide)e(a)i(step)f(to)m(w)m(ards)g (the)g(understanding)e(of)i(the)g(phase)g(co)s(existence)h(for)e(a)i (class)118 3189 y(of)35 b(mo)s(dels)f(broader)h(than)f(the)i (ferromagnetic)f(Ising)f(mo)s(dels.)53 b(Before)36 b(stating)f(the)h (main)e(results)118 3297 y(of)c(the)g(pap)s(er,)f(w)m(e)h(discuss)e (some)i(op)s(en)f(problems)f(and)h(summarize)f(the)i(di\016culties)d (whic)m(h)i(hinder)118 3405 y(the)i(extension)f(of)g(the)h Fy(L)991 3372 y Fx(1)1067 3405 y FA(theory)g(to)g(more)f(general)h(mo)s (dels.)218 3560 y(As)26 b(will)d(b)s(e)i(explained)f(later,)j(the)f (actual)g(results)f(on)g(phase)h(co)s(existence)h(are)f(v)-5 b(alid)24 b(for)h(a)i(limited)118 3668 y(class)34 b(of)g(microscopic)g (mo)s(dels,)g(namely)g(the)g(random)f(cluster)h(mo)s(del)f(with)g (\014nite)g(range)i(in)m(terac-)118 3776 y(tions.)49 b(The)33 b(description)e(of)j(more)f(subtle)g(phenomena)f(whic)m(h)g(o) s(ccur)i(in)e(ev)m(eryda)m(y)i(life,)f(or)h(whic)m(h)118 3884 y(are)26 b(observ)m(ed)f(in)f(exp)s(erimen)m(ts,)i(w)m(ould)e (require)g(the)h(in)m(v)m(estigation)g(of)h(more)f(realistic)f(mo)s (dels.)38 b(One)118 3992 y(of)d(the)g(most)h(curren)m(t)e(examples)h (of)g(phase)g(co)s(existence,)i(the)e(liquid/v)-5 b(ap)s(or)32 b(co)s(existence,)37 b(has)d(no)118 4099 y(rigorous)i(coun)m(terpart)i (\(with)e(the)h(exception)g(of)h(the)f(Widom)f(Ro)m(wlinson)g(mo)s(del) g(for)g(whic)m(h)g(the)118 4207 y(W)-8 b(ul\013)41 b(construction)g (should)f(b)s(e)h(a)h(straigh)m(tforw)m(ard)f(consequence)h(of)g(the)f (FK)h(corresp)s(ondence)118 4315 y([CCK)o(,)37 b(GLM)q(]\).)59 b(In)36 b(fact,)j(ev)m(en)e(the)g(primary)e(issue)g(of)i(the)f (liquid/v)-5 b(ap)s(or)33 b(phase)k(transition)e(has)118 4423 y(b)s(een)30 b(deriv)m(ed)f(only)h(for)g(a)h(limited)d(class)i(of) h(mo)s(dels.)39 b(A)31 b(discussion)c(on)k(the)f(p)s(ossible)e (implications)118 4531 y(of)e(the)h(recen)m(t)g(breakthrough)e([LMP])i (on)e(the)i(liquid/v)-5 b(ap)s(or)22 b(phase)k(transition)f(is)g(p)s (ostp)s(oned)f(to)j(re-)118 4639 y(mark)22 b(2.1.)39 b(More)23 b(generally)-8 b(,)24 b(the)e(study)g(of)g(mo)s(dels)f(go)m (v)m(erned)i(b)m(y)g(the)f(Pirogo)m(v)h(Sinai)d(Theory)i(w)m(ould)118 4747 y(shed)33 b(ligh)m(t)g(on)h(in)m(teresting)f(ph)m(ysical)g(mec)m (hanisms)g(whic)m(h)g(ha)m(v)m(e)i(still)c(not)k(b)s(een)e(thoroughly)g (ana-)118 4855 y(lyzed.)50 b(F)-8 b(or)34 b(example,)g(for)g(some)g(m)m (ulti-phase)e(mo)s(dels)g(without)h(symmetric)f(phases,)i(one)g(should) p 118 4932 499 4 v 218 5024 a Fw(Date)6 b FE(:)26 b(Jan)n(uary)g(19,)h (2001.)218 5115 y(1991)i Fw(Mathematics)g(Subje)l(ct)f(Classi\014c)l (ation.)39 b FE(82B20,)28 b(76B45.)218 5206 y Fw(Key)g(wor)l(ds)g(and)g (phr)l(ases.)40 b FE(Ising)26 b(Mo)r(del,)h(Surface)f(tension.)218 5298 y(I)d(am)f(v)n(ery)g(grateful)j(to)e(D.)g(Io\013e,)i(E.)e (Presutti,)i(R.)e(F)-6 b(ernandez,)23 b(C.)h(P\014ster)g(and)f(Y.)g(V) -6 b(elenik)22 b(for)i(man)n(y)e(in)n(teresting)118 5389 y(discussions)35 b(and)d(suggestions.)59 b(I)33 b(w)n(ould)g(also)i (lik)n(e)e(to)h(thank)e(the)h(organizers)i(of)f(the)e Fw(IV-th)j(Br)l(azilian)g(Scho)l(ol)g(of)118 5480 y(Pr)l(ob)l(ability) 27 b FE(and)e(in)h(particular)g(V.)f(Sidora)n(vicius)i(for)f(their)g (in)n(vitation)g(to)g(presen)n(t)f(this)h(w)n(ork.)1872 5580 y Fx(1)p eop %%Page: 2 2 2 1 bop 118 45 a Fx(2)1495 b(T.)23 b(BODINEA)n(U)118 366 y FA(observ)m(e)32 b(b)s(et)m(w)m(een)f(t)m(w)m(o)i(phases)d(the)h (o)s(ccurrence)h(of)f(an)g(in)m(termediate)f(la)m(y)m(er)i(of)f(a)h (third)d(phase)h(\(see)118 474 y([MMRS])39 b(for)e(a)i(discussion)c(of) j(this)f(phenomenon)g(in)g(the)h(case)h(of)f(the)h(large)f Fv(q)i FA(P)m(otts)g(mo)s(del)d(at)118 582 y(the)g(critical)f(p)s(oin)m (t\).)61 b(Nev)m(ertheless,)39 b(ev)m(en)f(if)e(the)i(bulk)d(prop)s (erties)g(are)j(w)m(ell)e(understo)s(o)s(d)f(in)h(the)118 690 y(con)m(text)30 b(of)e(Pirogo)m(v)h(Sinai)d(Theory)-8 b(,)29 b(the)f(surface)g(prop)s(erties)f(and,)h(more)h(precisely)-8 b(,)28 b(a)g(microscopic)118 798 y(deriv)-5 b(ation)29 b(of)i(the)f(W)-8 b(ul\013)30 b(construction)g(remain)f(an)i(op)s(en)e (problem.)218 906 y(In)c(the)g Fy(L)533 873 y Fx(1)604 906 y FA(approac)m(h,)i(the)f(phase)f(co)s(existence)h(is)f(analyzed)g (b)m(y)h(p)s(erforming)d(a)j(series)f(of)h(lo)s(caliza-)118 1014 y(tions)e(from)g(the)h(macroscopic)h(lev)m(el)e(to)h(the)g (microscopic)f(lev)m(el)h(in)e(order)h(to)i(relate)f(the)g(macroscopic) 118 1122 y(equilibrium)f(crystal)k(shap)s(es)f(to)i(the)f(surface)g (tension,)h(whic)m(h)d(is)i(de\014ned)f(in)g(terms)h(of)g(microscopic) 118 1230 y(quan)m(tities.)64 b(This)37 b(strategy)j(can)e(b)s(e)g (essen)m(tially)g(implemen)m(ted)f(on)h(a)h(coarse)g(grained)f(lev)m (el)g(and)118 1338 y(therefore)i(do)s(es)f(not)h(rely)f(on)g(the)h (microscopic)f(structure)g(of)h(the)f(mo)s(del.)67 b(Nev)m(ertheless,) 43 b(it)c(re-)118 1446 y(quires)c(the)i(v)-5 b(alidit)m(y)35 b(of)h(a)h(coarse)h(grained)d(represen)m(tation)i(of)f(the)h(mo)s(del)e (whic)m(h)h(k)m(eeps)h(trac)m(k)g(of)118 1554 y(the)29 b(lo)s(cal)f(order)g(parameter)h(and)f(ensures)g(some)h(decoupling)e (prop)s(erties.)39 b(W)-8 b(e)30 b(refer)e(to)i([BIV1)q(])f(for)118 1662 y(a)i(presen)m(tation)f(of)h(the)f Fy(L)1027 1629 y Fx(1)1103 1662 y FA(theory)g(in)f(a)i(general)g(framew)m(ork.)218 1770 y(This)19 b(sem)m(blance)i(of)h(generalit)m(y)f(su\013ers)g(from)g (an)g(imp)s(ortan)m(t)f(exception.)38 b(Once)21 b(the)h(in)m(terface)g (has)118 1877 y(b)s(een)j(lo)s(calized)f(on)i(a)g(mesoscopic)g(lev)m (el,)g(the)g(precise)f(surface)g(tension)g(factor)h(should)e(b)s(e)h (extracted)118 1985 y(from)40 b(some)h(coarse)h(grained)d(information.) 70 b(Therefore,)43 b(the)e(structure)f(of)h(the)f(coarse)i(graining)118 2093 y(b)s(ecomes)36 b(essen)m(tial)f(in)f(order)h(to)i(relate)f(the)f (mesoscopic)h(lev)m(el)f(to)i(the)e(microscopic)g(information)118 2201 y(whic)m(h)43 b(leads)h(to)i(the)e(surface)h(tension.)83 b(The)44 b(previous)f(pro)s(ofs)g(of)i(the)g(phase)f(co)s(existence)i (for)118 2309 y(Bernoulli)32 b(p)s(ercolation)h([Ce];)k(for)d(\014nite) f(range)h(Ising)f(mo)s(del)g([B1)q(,)h(CePi1,)g(BIV2)q(];)j(and)c(for)h (P)m(otts)118 2417 y(mo)s(del)39 b([CePi2])i(rely)e(crucially)f(on)i (Pisztora's)h(coarse)g(graining)e([Pi)o(].)71 b(This)38 b(coarse)k(graining)c(is)118 2525 y(a)d(fundamen)m(tal)f(to)s(ol)g(for) h(the)f(study)g(of)h(the)g(Ising/P)m(otts)g(mo)s(del)f(in)f(a)i(non)f (p)s(erturbativ)m(e)g(regime)118 2633 y(\(up)40 b(to)g(the)h(slab)e(p)s (ercolation)g(threshold\).)69 b(It)40 b(describ)s(es)f(the)h(\\bac)m (kb)s(one")h(of)f(the)h(Ising/P)m(otts)118 2741 y(spin)30 b(con\014gurations)i(in)f(terms)h(of)g(a)h(cluster)e(in)g(the)h(FK)h (represen)m(tation.)46 b(Th)m(us,)32 b(in)e(the)j(previous)118 2849 y(pro)s(ofs,)28 b(the)g(surface)g(tension)f(w)m(as)h(rede\014ned)f (in)f(terms)i(of)g(the)g(random)f(cluster)g(mo)s(del)g(in)f(order)i(to) 118 2957 y(b)s(e)i(related)g(to)h(the)g(coarse)g(graining.)218 3065 y(This)43 b(approac)m(h)i(w)m(ould)e(seem)j(to)f(limit)e(the)i (generalization)f(to)i(mo)s(dels)d(for)i(whic)m(h)e(the)i(FK)118 3173 y(corresp)s(ondence)20 b(do)s(es)g(not)h(hold.)36 b(F)-8 b(urthermore,)23 b(the)e(previous)e(pro)s(ofs)g(are)i(based)g (up)s(on)e(correlation)118 3281 y(inequalities)35 b(whic)m(h)h(are)i (not)f(satis\014ed)g(b)m(y)g(general)g(mo)s(dels.)61 b(Therefore,)39 b(the)e(analysis)f(of)i(phase)118 3388 y(co)s(existence)d(for)f(mo)s(dels)e(in)h(the)h(Pirogo)m(v)h(Sinai)d (theory)i(w)m(ould)f(need)g(to)i(dev)m(elop)f(di\013eren)m(t)g(to)s (ols)118 3496 y(and)21 b(to)i(devise)e(a)h(more)g(robust)f(analysis)f (of)i(surface)g(tension.)37 b(It)22 b(w)m(ould)f(b)s(e)g(in)m (teresting)g(to)h(in)m(tro)s(duce)118 3604 y(a)38 b(tractable)h (macroscopic)f(de\014nition)d(of)j(surface)g(tension)f(whic)m(h)f(do)s (es)h(not)h(rely)f(on)h(correlation)118 3712 y(inequalities)28 b(and)i(on)g(the)g(FK)h(represen)m(tation.)218 3867 y(In)37 b(this)g(pap)s(er)f(more)i(mo)s(dest)g(questions)f(are)h(addressed.)62 b(First,)40 b(an)e(approac)m(h)g(of)g(the)g(W)-8 b(ul\013)118 3975 y(construction)30 b(is)f(presen)m(ted)h(for)g(the)g(Ising)f(mo)s (del)g(without)g(using)g(the)h(FK)g(corresp)s(ondence.)40 b(This)118 4083 y(analysis)h(is)g(limited)e(to)k(lo)m(w)f(temp)s (eratures.)75 b(Nev)m(ertheless,)46 b(since)41 b(it)h(is)f(mainly)f (based)h(on)h(the)118 4191 y(P)m(eierls)d(condition,)j(parts)e(of)g(it) g(should)e(b)s(e)h(easy)i(to)g(transp)s(ose)f(in)f(other)h(con)m (texts.)72 b(In)39 b(a)i(\014nal)118 4299 y(section,)30 b(this)e(metho)s(d)h(is)f(generalized)h(in)f(order)g(to)i(deriv)m(e)f (the)g(W)-8 b(ul\013)29 b(construction)g(for)g(Kac)h(Ising)118 4407 y(mo)s(dels.)218 4515 y(The)43 b(\014rst)g(step)i(is)e(to)h(in)m (tro)s(duce)f(a)i(new)e(coarse)i(graining)e(appropriate)g(for)g(the)h Fy(L)3299 4482 y Fx(1)3388 4515 y FA(theory)-8 b(.)118 4623 y(Then)32 b(w)m(e)h(deduce)f(from)h(a)g(general)g(exp)s(onen)m (tial)e(tigh)m(tness)i(theorem)g(the)g(phenomenon)f(of)h(phase)118 4731 y(segregation,)k(i.e.)51 b(the)35 b(fact)g(that)f(phase)g(co)s (existence)h(do)s(es)f(not)g(o)s(ccur)g(b)m(y)g(the)g(creation)h(of)f (man)m(y)118 4839 y(small)25 b(droplets)h(of)h(one)g(phase)f(scattered) i(in)e(the)h(other,)h(but)e(b)m(y)h(a)g(macroscopic)g(phase)f (separation.)118 4947 y(Alternativ)m(ely)-8 b(,)30 b(this)f(phenomenon) g(manifests)g(itself)g(b)m(y)h(surface)g(order)f(large)h(deviations)f (\(see)i([Sc,)118 5055 y(Pi)o(]\).)39 b(This)23 b(\014rst)g(part)h(is)f (only)h(based)f(up)s(on)g(the)h(P)m(eierls)g(condition)e(and)i(should)e (b)s(e)i(straigh)m(tforw)m(ard)118 5163 y(to)31 b(generalize)g(\(ev)m (en)g(in)e(the)i(case)g(of)g(m)m(ulti-phase)e(mo)s(dels\).)218 5271 y(In)40 b(a)h(second)g(step,)j(the)d(equilibrium)c(crystal)j(shap) s(es)g(are)i(deriv)m(ed.)71 b(The)41 b(pro)s(of)f(follo)m(ws)g(the)118 5378 y(general)k(sc)m(heme)g(of)g(the)g Fy(L)1111 5345 y Fx(1)1200 5378 y FA(theory)-8 b(,)48 b(but)43 b(it)g(is)g(implemen)m (ted)f(with)h(the)h(new)f(coarse)i(graining)p eop %%Page: 3 3 3 2 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)782 b(3)118 366 y FA(directly)39 b(on)g(the)h(spin)e (lev)m(el.)69 b(A)m(t)41 b(this)d(stage,)44 b(the)c(existence)g(of)g (surface)g(tension)f(\(kno)m(wn)h(from)118 474 y(correlation)30 b(inequalities\))e(and)i(the)g(symmetry)g(b)s(et)m(w)m(een)h(the)g (phases)f(\(spin)f(\015ip\))f(come)k(in)m(to)e(pla)m(y)-8 b(.)218 582 y(In)29 b(the)i(last)f(part,)g(the)h(previous)e(strategy)i (is)f(up)s(dated)e(to)j(the)g(con)m(text)h(of)f(the)f(Kac)h(Ising)e(mo) s(d-)118 690 y(els)j(with)g(long)g(but)g(\014nite)g(range)h(in)m (teractions.)47 b(The)32 b(\014rst)g(deriv)-5 b(ation)32 b(of)h(the)f(W)-8 b(ul\013)33 b(construction)118 798 y(for)j(Kac)g(Ising)e(mo)s(dels)g(w)m(as)i(obtained)f(b)m(y)h([ABCP,)g (BCP])g(\(see)g(also)g([AlBe])g(for)g(anisotropic)e(in-)118 906 y(teractions\).)75 b(In)41 b(these)g(w)m(orks,)k(the)c(in)m (teraction)h(w)m(as)g(rescaled)f(with)f(the)i(n)m(um)m(b)s(er)e(of)h (particles)118 1014 y(\()p Fv(N)e Fu(\030)28 b Fv(\015)416 981 y Ft(\000)p Fx(1)p Ft(\000)p Fs(\017)594 1014 y FA(\))33 b(and)e(the)i(phase)f(co)s(existence)h(stemmed)f(from)g(the)h(pro)s(of) e(of)i(the)f(\000-con)m(v)m(ergence)j(of)118 1122 y(functionals)29 b(asso)s(ciated)j(to)f(the)h(con)m(tin)m(uous)e(limit)f(of)i(the)g(mo)s (del.)41 b(The)31 b(functional)e(framew)m(ork)i(of)118 1230 y(the)i Fy(L)332 1197 y Fx(1)410 1230 y FA(theory)g(w)m(as)g(in)m (tro)s(duced)e(in)h(these)h(pap)s(ers)f(and)g(the)h(imp)s(ortance)f(of) h(the)g(geometric)g(mea-)118 1338 y(sure)28 b(theory)i(and)e(of)h (related)g(compactness)h(prop)s(erties)d(w)m(as)j(emphasized.)39 b(In)28 b([BBBP)r(,)h(BBP],)h(the)118 1446 y(prediction)h(of)j(the)f(v) -5 b(an)33 b(der)g(W)-8 b(aals)34 b(theory)f(of)h(surface)f(tension)f (is)g(reco)m(v)m(ered)j(when)d(the)i(range)f(of)118 1554 y(the)c(in)m(teraction)f(div)m(erges)g(to)i(in\014nit)m(y)-8 b(.)38 b(More)29 b(precisely)-8 b(,)28 b(the)h(probabilistic)c(cost)k (of)g(a)g(macroscopic)118 1662 y(in)m(terface)f(w)m(as)f(pro)m(v)m(en)g (to)h(b)s(e)e(exp)s(onen)m(tially)f(small)g(with)h(a)h(factor)h(prop)s (ortional)d(to)j(the)f(p)s(erimeter)118 1770 y(of)d(the)f(in)m(terface) h(times)f(the)h(v)-5 b(an)23 b(der)g(W)-8 b(aals)24 b(surface)f (tension.)38 b(As)23 b(a)h(consequence,)i(the)d(equilibrium)118 1877 y(crystal)35 b(shap)s(es)g(con)m(v)m(erge)i(to)g(a)e(sphere)g(in)f (the)i(Leb)s(o)m(witz)f(and)g(P)m(enrose)h(limit.)53 b(F)-8 b(or)37 b(\014nite)d(range)118 1985 y(in)m(teraction)25 b(only)f(a)h(rough)f(description)e(of)j(the)g(crystals)f(w)m(as)i (obtained.)38 b(Building)21 b(on)k(the)g(previous)118 2093 y(results,)35 b(the)g(presen)m(t)g(pap)s(er)f(completes)h(the)g(W) -8 b(ul\013)35 b(construction)f(for)h(\014nite)f(range)h(in)m (teractions.)118 2201 y(The)30 b(main)f(ingredien)m(t)g(is)g(the)i (deriv)-5 b(ation)29 b(of)h(the)h(surface)f(tension)g(from)g(an)g (appro)m(ximate)g(expres-)118 2309 y(sion)g(de\014ned)f(only)h(on)h(a)g (coarse)h(grained)e(lev)m(el.)42 b(As)31 b(a)g(consequence)g(of)g ([BBBP)r(],)g(the)g(sequence)g(of)118 2419 y(surface)h(tensions)f (de\014ned)g(for)h(an)m(y)h(range)f(of)g(the)h(in)m(teraction)2391 2383 y Fx(1)p 2389 2398 41 4 v 2389 2450 a Fs(\015)2471 2419 y FA(con)m(v)m(erges)h(to)f(the)f(isotropic)g(v)-5 b(an)118 2535 y(der)30 b(W)-8 b(aals)31 b(surface)f(tension.)1372 2760 y(2.)46 b Fz(Models)33 b(and)h(resul)-6 b(ts)118 2922 y FA(2.1.)47 b FF(Ising)37 b(mo)s(del.)45 b FA(Let)32 b(\003)h(b)s(e)e(a)h(\014nite)f(domain)g(of)i Fy(Z)2106 2889 y Fs(d)2142 2922 y FA(,)f(for)g Fv(d)c Fr(>)g FA(2.)46 b(Eac)m(h)33 b(site)f Fv(i)g FA(in)f(\003)h(indexes)f(a)118 3030 y(spin)h Fv(\033)366 3044 y Fs(i)427 3030 y FA(whic)m(h)g(tak)m (es)j(v)-5 b(alues)33 b Fu(\006)p FA(1.)50 b(The)33 b(spin)e (con\014gurations)i Fu(f)p Fv(\033)2463 3044 y Fs(i)2491 3030 y Fu(g)2536 3044 y Fs(i)p Ft(2)p Fx(\003)2694 3030 y FA(ha)m(v)m(e)i(a)f(statistical)f(w)m(eigh)m(t)118 3138 y(determined)c(b)m(y)h(the)h(Hamiltonian)815 3337 y Fv(H)902 3299 y Fx(\026)-39 b Fs(\033)945 3337 y FA(\()p Fv(\033)s FA(\))26 b(=)f Fu(\000)1273 3275 y FA(1)p 1273 3316 46 4 v 1273 3399 a(2)1364 3251 y Fq(X)1343 3447 y Fs(i;j)t Ft(2)p Fx(\003)1531 3337 y Fv(J)9 b FA(\()p Fv(i)21 b Fu(\000)f Fv(j)5 b FA(\))p Fv(\033)1897 3351 y Fs(i)1926 3337 y Fv(\033)1978 3351 y Fs(j)2034 3337 y Fu(\000)2210 3251 y Fq(X)2125 3447 y Fs(i)p Ft(2)p Fx(\003)p Fs(;j)t Ft(2)p Fx(\003)2394 3429 y Fp(c)2440 3337 y Fv(J)k FA(\()p Fv(i)21 b Fu(\000)f Fv(j)5 b FA(\))p Fv(\033)2806 3351 y Fs(i)2840 3337 y FA(\026)-50 b Fv(\033)2887 3351 y Fs(j)2939 3337 y Fv(;)118 3599 y FA(where)34 b(\026)-50 b Fv(\033)29 b FA(=)c Fu(f)5 b FA(\026)-50 b Fv(\033)654 3613 y Fs(i)682 3599 y Fu(g)727 3613 y Fs(i)p Ft(2)p Fx(\003)847 3594 y Fp(c)914 3599 y FA(are)30 b(the)g(b)s(oundary)e (conditions)g(outside)h(\003)h(and)f Fv(J)39 b FA(are)30 b(ferromagnetic)g(\014nite)118 3706 y(range)h(coupling)d(constan)m(ts,) k(i.e.)41 b Fv(J)34 b Fr(>)25 b FA(0)31 b(and)f(there)g(is)g Fv(R)c(>)f FA(0)30 b(suc)m(h)g(that)h Fv(J)9 b FA(\()p Fv(i)p FA(\))27 b(=)e(0)31 b(if)e Fu(k)p Fv(i)p Fu(k)3302 3720 y Ft(1)3403 3706 y Fv(>)c(R)q FA(.)218 3814 y(The)30 b(Gibbs)e(measure)j(asso)s(ciated)f(to)i(the)e(spin)f(system)h(with)f (b)s(oundary)g(conditions)k(\026)-50 b Fv(\033)34 b FA(is)856 4013 y Fu(8)p Fv(\033)28 b FA(=)d Fu(f)p Fv(\033)1180 4027 y Fs(x)1225 4013 y Fu(g)1270 4027 y Fs(x)p Ft(2)p Fx(\003)1410 4013 y Fv(;)197 b(\026)1691 3976 y Fx(\026)-39 b Fs(\033)1687 4036 y(\014)s(;)p Fx(\003)1803 4013 y FA(\()p Fv(\033)s FA(\))26 b(=)2126 3952 y(1)p 2060 3992 178 4 v 2060 4075 a Fv(Z)2132 4044 y Fx(\026)-38 b Fs(\033)2122 4105 y(\014)s(;)p Fx(\003)2263 4013 y FA(exp)2417 3939 y Fq(\000)2458 4013 y Fu(\000)p Fv(\014)5 b(H)2672 3976 y Fx(\026)-39 b Fs(\033)2715 4013 y FA(\()p Fv(\033)s FA(\))2840 3939 y Fq(\001)2898 4013 y Fv(;)118 4257 y FA(where)32 b Fv(\014)37 b FA(is)32 b(the)g(in)m(v)m(erse)g(of)h(the)f (temp)s(erature)g(\()p Fv(\014)i FA(=)2047 4221 y Fx(1)p 2040 4236 51 4 v 2040 4289 a Fs(T)2100 4257 y FA(\))f(and)f Fv(Z)2419 4224 y Fx(\026)-38 b Fs(\033)2409 4285 y(\014)s(;N)2571 4257 y FA(is)31 b(the)i(partition)e(function.)45 b(If)118 4374 y(the)36 b(b)s(oundary)e(conditions)g(are)i(uniformly)c(equal)j (to)i(1)f(\(resp)f Fu(\000)p FA(1\),)j(the)d(Gibbs)f(measure)i(will)d (b)s(e)118 4484 y(denoted)e(b)m(y)f Fv(\026)643 4445 y Fx(+)643 4513 y Fs(\014)s(;)p Fx(\003)789 4484 y FA(\(resp)g Fv(\026)1072 4445 y Ft(\000)1072 4513 y Fs(\014)s(;)p Fx(\003)1187 4484 y FA(\).)218 4640 y(Let)j Fy(D)443 4654 y Fs(N)549 4640 y FA(b)s(e)f(the)h(subset)f Fu(f\000)p Fv(N)5 b(;)15 b(:)g(:)g(:)i(;)e(N)10 b Fu(g)1639 4607 y Fs(d)1713 4640 y FA(of)33 b Fy(Z)1884 4607 y Fs(d)1920 4640 y FA(.)49 b(There)32 b(is)g(a)h(critical)f(v)-5 b(alue)32 b Fv(\014)3025 4654 y Fs(c)3093 4640 y FA(ab)s(o)m(v)m(e)i (whic)m(h)e(a)118 4748 y(breaking)e(of)g(symmetry)g(o)s(ccurs)g(in)f (the)i(thermo)s(dynamic)e(limit)802 4908 y Fu(8)p Fv(\014)h(>)25 b(\014)1081 4922 y Fs(c)1116 4908 y Fv(;)198 b FA(lim)1370 4969 y Fs(N)1480 4908 y Fv(\026)1535 4870 y Fx(+)1535 4938 y Fs(\014)s(;N)1665 4908 y FA(\()p Fv(\033)1752 4922 y Fx(0)1791 4908 y FA(\))26 b(=)f Fu(\000)15 b FA(lim)2065 4969 y Fs(N)2175 4908 y Fv(\026)2230 4870 y Ft(\000)2230 4938 y Fs(\014)s(;N)2360 4908 y FA(\()p Fv(\033)2447 4922 y Fx(0)2487 4908 y FA(\))25 b(=)g Fv(m)2723 4871 y Ft(\003)2723 4931 y Fs(\014)2795 4908 y Fv(>)g FA(0)15 b Fv(:)499 b FA(\(2.1\))118 5117 y(F)-8 b(urthermore,)39 b(in)d(the)h(thermo)s(dynamic)e(limit)g(the)j(measures)e Fv(\026)2452 5079 y Fx(+)2452 5146 y Fs(\014)s(;N)2619 5117 y FA(and)g Fv(\026)2857 5079 y Ft(\000)2857 5146 y Fs(\014)s(;N)3024 5117 y FA(con)m(v)m(erge)j(to)f(t)m(w)m(o)118 5259 y(distinct)e(Gibbs)g(measures)h Fv(\026)1177 5220 y Fx(+)1177 5288 y Fs(\014)1273 5259 y FA(and)f Fv(\026)1511 5220 y Ft(\000)1511 5288 y Fs(\014)1608 5259 y FA(whic)m(h)g(are)h (measures)g(on)h(the)f(space)h Fu(f\006)p FA(1)p Fu(g)3183 5226 y Fo(Z)3234 5202 y Fp(d)3269 5259 y FA(.)61 b(Eac)m(h)38 b(of)118 5372 y(these)31 b(measures)f(represen)m(ts)g(a)h(pure)e (state.)p eop %%Page: 4 4 4 3 bop 118 45 a Fx(4)1495 b(T.)23 b(BODINEA)n(U)218 366 y FA(W)-8 b(e)22 b(are)f(going)g(to)g(de\014ne)f(the)h(surface)g (tension.)36 b(Let)19 b Fv(~)-42 b(n)20 b FA(b)s(e)g(a)h(v)m(ector)h (in)e Fy(S)2708 333 y Fs(d)p Ft(\000)p Fx(1)2854 366 y FA(suc)m(h)g(that)f Fv(~)-43 b(n)q Fu(\001)m Fv(~)i(e)3360 380 y Fx(1)3425 366 y Fv(>)3561 331 y Fx(1)p 3531 346 96 4 v 3531 355 a Ft(p)p 3590 355 37 3 v 57 x Fs(d)3636 366 y FA(.)118 506 y(Let)38 b(\003)351 520 y Fs(N)455 506 y FA(=)e Fu(f)p Fv(i)i FA(=)e(\()p Fv(i)849 520 y Fx(1)889 506 y Fv(;)15 b(:)g(:)g(:)i(;)e(i)1122 521 y Fs(d)1163 506 y FA(\))37 b Fu(2)g Fy(Z)1398 473 y Fs(d)1470 506 y Fu(j)g(8)p Fv(k)j Fr(>)c FA(2)p Fv(;)107 b Fu(j)p Fv(i)2010 521 y Fs(k)2053 506 y Fu(j)37 b Fr(6)g Fv(N)10 b Fu(g)37 b FA(and)g(\001)2648 520 y Fs(N)2752 506 y FA(b)s(e)g(a)g(sequence)h(of)f(\014nite)118 614 y(subsets)30 b(of)g(\003)599 628 y Fs(N)697 614 y FA(suc)m(h)g(that)1242 769 y Fu(f)p Fv(i)c Fu(2)e Fy(Z)1494 732 y Fs(d)1556 769 y Fu(j)91 b(j)n Fv(~)-43 b(n)20 b Fu(\001)g Fv(i)p Fu(j)26 b Fr(6)f Fv(f)10 b FA(\()p Fv(N)g FA(\))p Fu(g)26 b(\032)f FA(\001)2446 783 y Fs(N)2513 769 y Fv(;)118 925 y FA(for)32 b(some)h(function)e Fv(f)41 b FA(suc)m(h)33 b(that)f Fv(f)10 b FA(\()p Fv(N)g FA(\))33 b(div)m(erges)f(as)g Fv(N)43 b FA(go)s(es)33 b(to)g(in\014nit)m(y)-8 b(.)44 b(The)32 b(mixed)f(b)s(oundary)118 1033 y(conditions)j(\026)-50 b Fv(\033)33 b FA(are)e(de\014ned)e(as)1018 1248 y Fu(8)p Fv(i)c Fu(2)g FA(\001)1287 1210 y Fs(c)1287 1270 y(N)1354 1248 y Fv(;)202 b FA(\026)-50 b Fv(\033)1628 1262 y Fs(i)1681 1248 y FA(=)1777 1092 y Fq(\()1850 1186 y FA(+1)p Fv(;)274 b FA(if)87 b Fv(~)-43 b(n)20 b Fu(\001)h Fv(i)k Fr(>)g FA(0)p Fv(;)1850 1316 y Fu(\000)p FA(1)p Fv(;)274 b FA(if)87 b Fv(~)-43 b(n)20 b Fu(\001)h Fv(i)k(<)g FA(0)p Fv(:)118 1496 y FA(The)33 b(partition)f(function)g(with)g(mixed)g(b)s(oundary)f (conditions)h(is)g(denoted)i(b)m(y)f Fv(Z)3021 1457 y Ft(\006)3014 1525 y Fs(\014)s(;)p Fx(\001)3136 1536 y Fp(N)3197 1496 y FA(\()n Fv(~)-43 b(n)p FA(\))33 b(and)g(the)118 1625 y(one)e(with)e(b)s(oundary)f(conditions)h(uniformly)e(equal)j(to)h (1)g(b)m(y)f Fv(Z)2372 1586 y Fx(+)2365 1654 y Fs(\014)s(;)p Fx(\001)2487 1665 y Fp(N)2549 1625 y FA(.)118 1814 y FF(De\014nition)35 b(2.1.)42 b Fn(The)32 b(surfac)-5 b(e)33 b(tension)g(in)f(the)g(dir)-5 b(e)g(ction)32 b Fv(~)-43 b(n)25 b Fu(2)g Fy(S)2481 1781 y Fs(d)p Ft(\000)p Fx(1)2606 1814 y Fn(,)32 b(with)f Fv(~)-43 b(n)19 b Fu(\001)d Fv(~)-41 b(e)3024 1828 y Fx(1)3089 1814 y Fv(>)25 b FA(0)p Fn(,)32 b(is)g(de\014ne)-5 b(d)118 1922 y(by)1140 2114 y Fv(\034)1180 2129 y Fs(\014)1227 2114 y FA(\()n Fv(~)-43 b(n)p FA(\))25 b(=)64 b(lim)1473 2174 y Fs(N)7 b Ft(!1)1708 2114 y Fu(\000)1789 2052 y FA(\()n Fv(~)-43 b(n)o(;)12 b(~)-42 b(e)1960 2066 y Fx(1)2001 2052 y FA(\))p 1789 2093 248 4 v 1805 2176 a Fv(N)1888 2150 y Fs(d)p Ft(\000)p Fx(1)2076 2114 y FA(log)2219 2036 y Fv(Z)2288 1998 y Ft(\006)2281 2065 y Fs(\014)s(;)p Fx(\001)2403 2076 y Fp(N)2464 2036 y FA(\()n Fv(~)f(n)p FA(\))p 2219 2093 371 4 v 2281 2182 a Fv(Z)2350 2144 y Fx(+)2343 2211 y Fs(\014)s(;)p Fx(\001)2465 2222 y Fp(N)2614 2114 y Fv(:)836 b FA(\(2.2\))218 2371 y(F)-8 b(or)42 b Fv(\014)49 b(>)44 b(\014)658 2385 y Fs(c)693 2371 y FA(,)h(the)d(surface)f(tension)g(is)g (uniformly)e(p)s(ositiv)m(e)h(on)i Fy(S)2643 2338 y Fs(d)p Ft(\000)p Fx(1)2810 2371 y FA(and)f(its)g(homogeneous)118 2479 y(extension)30 b(on)g Fy(R)706 2446 y Fs(d)812 2667 y Fu(8)p Fv(x)25 b Fu(2)f Fy(R)1085 2629 y Fs(d)1132 2667 y Fv(;)197 b(\034)1394 2682 y Fs(\014)1441 2667 y FA(\()p Fv(x)p FA(\))26 b(=)f Fu(k)p Fv(x)p Fu(k)1827 2681 y Fx(2)1882 2667 y Fv(\034)1922 2682 y Fs(\014)1984 2539 y Fq(\022)2126 2605 y Fv(x)p 2061 2646 183 4 v 2061 2729 a Fu(k)p Fv(x)p Fu(k)2203 2743 y Fx(2)2253 2539 y Fq(\023)2335 2667 y Fv(;)198 b(\034)2598 2682 y Fs(\014)2644 2667 y FA(\(0\))27 b(=)e(0)15 b Fv(;)118 2872 y FA(is)32 b(con)m(v)m(ex.)48 b(The)32 b(previous)e(prop)s(erties)h(of)i(surface)f (tension,)g(as)h(w)m(ell)e(as)i(its)f(existence)h(are)f(deriv)m(ed)118 2980 y(b)m(y)d(using)e(ferromagnetic)i(inequalities.)38 b(The)28 b(reader)h(is)f(referred)g(to)h([MMR)q(])g(for)g(a)g (comprehensiv)m(e)118 3088 y(discussion)f(on)i(surface)g(tension.)118 3270 y(2.2.)47 b FF(Kac)28 b(Ising)h(mo)s(del.)45 b FA(The)24 b(Kac)h(Ising)e(mo)s(del)h(is)f(a)i(ferromagnetic)g(spin)e(system)h (with)g(in)m(terac-)118 3377 y(tions)i(tuned)g(b)m(y)g(a)h(scaling)e (parameter)i Fv(\015)5 b FA(.)40 b(Let)27 b Fv(J)35 b FA(b)s(e)26 b(a)h(non-negativ)m(e)h(smo)s(oth)e(function)f(supp)s (orted)118 3485 y(b)m(y)33 b([)p Fu(\000)p FA(1)p Fv(;)15 b FA(1])35 b(and)e(suc)m(h)g(that)1121 3412 y Fq(R)1164 3517 y Fo(R)1212 3498 y Fp(d)1267 3485 y Fv(J)9 b FA(\()p Fu(j)p Fv(r)s Fu(j)p FA(\))15 b Fv(dr)35 b FA(=)30 b(1.)50 b(F)-8 b(or)34 b(an)m(y)g Fv(\015)h(>)30 b FA(0)k(the)f(Kac)h(p)s(oten) m(tials)f(are)h(de\014ned)118 3593 y(b)m(y)1191 3751 y Fu(8)p Fv(i)25 b Fu(2)g Fy(Z)1449 3713 y Fs(d)1485 3751 y Fv(;)197 b(J)1757 3765 y Fs(\015)1802 3751 y FA(\()p Fv(i)p FA(\))27 b(=)d Fv(\015)2077 3713 y Fs(d)2118 3751 y Fv(J)9 b FA(\()p Fv(\015)c Fu(j)p Fv(i)p Fu(j)p FA(\))15 b Fv(:)118 3906 y FA(F)-8 b(or)27 b(simplicit)m(y)-8 b(,)25 b Fv(\015)31 b FA(is)26 b(c)m(hosen)g(as)h(2)1311 3873 y Ft(\000)p Fs(g)1432 3906 y FA(with)e Fv(g)k Fu(2)c Fy(N)7 b FA(.)45 b(T)-8 b(o)26 b(emphasize)g(the)h(dep)s(endence)e(on)h (the)g(scaling)118 4014 y(parameter,)35 b(the)e(Gibbs)e(measure)i(on)g (\003)h(at)f(in)m(v)m(erse)g(temp)s(erature)g Fv(\014)39 b FA(and)32 b(with)g(b)s(oundary)f(condi-)118 4122 y(tions)k(\026)-50 b Fv(\033)33 b FA(is)d(denoted)g(b)m(y)g Fv(\026)1046 4089 y Fx(\026)-39 b Fs(\033)1042 4150 y(\014)s(;\015)t(;)p Fx(\003)1218 4122 y FA(.)218 4338 y(F)-8 b(or)26 b(an)m(y)g Fv(\015)31 b(>)25 b FA(0,)i(a)f(critical)f(temp)s(erature)h Fv(\014)1749 4352 y Fs(c)1784 4338 y FA(\()p Fv(\015)5 b FA(\))26 b(\(corresp)s(onding)e(to)j(the)f(non-uniqueness)d(of)j(the) 118 4446 y(in\014nite)i(Gibbs)h(measure\))i(is)e(asso)s(ciated)i(to)g (the)g(system.)40 b(It)31 b(is)e(pro)m(v)m(ed)i(in)e([CaPr,)h(BZ])h (that)1389 4608 y(lim)1380 4666 y Fs(\015)t Ft(!)p Fx(0)1556 4608 y Fv(\014)1607 4622 y Fs(c)1642 4608 y FA(\()p Fv(\015)5 b FA(\))26 b(=)f Fv(\014)1942 4570 y Fx(mf)1937 4630 y Fs(c)2052 4608 y FA(=)g(1)15 b Fv(;)118 4823 y FA(where)30 b Fv(\014)437 4790 y Fx(mf)432 4845 y Fs(c)553 4823 y FA(denotes)h(the)g(critical)e(temp)s(erature)i(of)g(the)f(mean)h (\014eld)e(system.)42 b(F)-8 b(or)32 b(an)m(y)f Fv(\014)g(>)25 b FA(1,)31 b(this)118 4932 y(implies)25 b(the)j(existence)g(of)g(t)m(w) m(o)h(distinct)d(Gibbs)g(measures)i Fv(\026)2262 4894 y Fx(+)2262 4961 y Fs(\014)s(;\015)2396 4932 y FA(and)f Fv(\026)2625 4894 y Ft(\000)2625 4961 y Fs(\014)s(;\015)2760 4932 y FA(for)g(su\016cien)m(tly)g(small)f Fv(\015)5 b FA(.)118 5046 y(In)30 b(particular,)f(the)h(phase)g(transition)f(is)h (c)m(haracterized)h(b)m(y)f(a)h(sp)s(on)m(taneous)f(magnetization)784 5201 y Fu(8)p Fv(\014)g(>)25 b FA(1)p Fv(;)15 b Fu(9)p Fv(\015)1195 5216 y Fs(\014)1268 5201 y Fv(>)25 b FA(0)p Fv(;)15 b Fu(8)p Fv(\015)31 b(<)25 b(\015)1721 5216 y Fs(\014)1768 5201 y Fv(;)197 b(\026)2045 5163 y Fx(+)2045 5231 y Fs(\014)s(;\015)2152 5201 y FA(\()p Fv(\033)2239 5215 y Fx(0)2279 5201 y FA(\))25 b(=)g Fv(m)2515 5164 y Ft(\003)2515 5224 y Fs(\014)s(;\015)2647 5201 y Fv(>)g FA(0)15 b Fv(:)647 b FA(\(2.3\))118 5363 y(When)30 b Fv(\015)36 b FA(v)-5 b(anishes,)30 b Fv(m)929 5330 y Ft(\003)929 5391 y Fs(\014)s(;\015)1066 5363 y FA(con)m(v)m(erges)i(to) g(the)e(mean)h(\014eld)e(magnetization)i Fv(m)2852 5330 y Ft(\003)2852 5391 y Fs(\014)2899 5363 y FA(.)42 b(In)29 b(passing,)h(notice)118 5480 y(that)h(a)g(stronger)f(result)g(has)g(b)s (een)f(deriv)m(ed)h(in)f([BMP)q(])p eop %%Page: 5 5 5 4 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)782 b(5)118 366 y FF(Theorem)35 b(2.1.)42 b Fn(F)-7 b(or)34 b(any)g Fv(\014)d(>)26 b FA(1)p Fn(,)34 b(ther)-5 b(e)34 b(is)f Fv(\015)1770 381 y Fs(\014)1843 366 y Fv(>)26 b FA(0)33 b Fn(such)h(that)g(for)g(any)f Fv(\015)f(<)25 b(\015)2954 381 y Fs(\014)3002 366 y Fn(,)33 b(any)g(tr)-5 b(anslation)118 481 y(invariant)34 b(Gibbs)e(me)-5 b(asur)g(e)34 b(is)f(a)g(c)-5 b(onvex)33 b(c)-5 b(ombination)34 b(of)f Fv(\026)2260 443 y Fx(+)2260 510 y Fs(\014)s(;\015)2400 481 y Fn(and)g Fv(\026)2631 443 y Ft(\000)2631 510 y Fs(\014)s(;\015)2738 481 y Fn(.)218 653 y FA(This)k(assertion)i(sho)m (ws)g(that,)k(as)c(in)f(the)i(v)-5 b(an)39 b(der)f(W)-8 b(aals)40 b(Theory)-8 b(,)42 b(there)e(are)f(only)g(t)m(w)m(o)h(pure) 118 761 y(phases)30 b(for)g(su\016cien)m(tly)f(long)h(range)h(in)m (teractions.)118 939 y(2.3.)47 b FF(The)25 b(functional)g(setting.)45 b FA(W)-8 b(e)23 b(consider)e(a)h(general)g(ferromagnetic)g(Ising)e(mo) s(del)h(as)h(de\014ned)118 1047 y(in)44 b(Subsections)f(2.1)j(and)e (2.2.)85 b(In)44 b(order)g(to)h(enforce)g(phase)g(co)s(existence,)k (the)c(measure)g Fv(\026)3532 1009 y Fx(+)3532 1076 y Fs(\014)s(;N)118 1175 y FA(is)c(conditioned)g(b)m(y)h(the)g(ev)m(en)m (t)i(that)e(the)h(a)m(v)m(eraged)h(magnetization)e(is)f(at)m(ypical,)46 b(i.e.)3326 1101 y Fq(\010)3379 1175 y FF(M)3479 1189 y Fs(N)3591 1175 y FA(=)249 1258 y Fx(1)p 128 1273 279 4 v 128 1327 a(\(2)p Fs(N)7 b Fx(+1\))370 1308 y Fm(3)431 1225 y Fq(P)527 1320 y Fs(i)p Ft(2)p Fo(D)640 1331 y Fp(N)723 1293 y Fv(\033)775 1307 y Fs(i)836 1293 y Fr(6)32 b Fv(m)1034 1220 y Fq(\011)1087 1293 y Fv(;)j FA(where)f Fv(m)h FA(is)f(a)h(constan)m(t)h(in)d(])24 b Fu(\000)f Fv(m)2409 1260 y Ft(\003)2409 1321 y Fs(\014)2456 1293 y Fv(;)15 b(m)2576 1260 y Ft(\003)2576 1321 y Fs(\014)2623 1293 y FA([.)54 b(The)34 b(problem)f(will)f(b)s(e)j(to)118 1430 y(c)m(haracterize)43 b(the)e(t)m(ypical)f(con\014gurations)g(of)h (the)g(conditional)f(measure)g Fv(\026)2885 1392 y Fx(+)2885 1460 y Fs(\014)s(;N)3015 1357 y Fq(\000)3084 1430 y Fu(\001)j(j)15 b FF(M)3291 1444 y Fs(N)3401 1430 y Fr(6)43 b Fv(m)3595 1357 y Fq(\001)3636 1430 y FA(.)118 1544 y(Before)31 b(stating)g(the)g(results,)e(let)h(us)g(in)m(tro)s(duce)f(the)i (macroscopic)g(setting.)218 1705 y(On)f(the)h(macroscopic)h(lev)m(el,)f (the)h(system)f(is)f(con\014ned)h(in)f(the)h(cub)s(e)2671 1681 y Fq(b)2664 1705 y Fy(D)49 b FA(=)26 b([)p Fu(\000)2959 1669 y Fx(1)p 2959 1684 36 4 v 2959 1736 a(2)3004 1705 y Fv(;)3055 1669 y Fx(1)p 3055 1684 V 3055 1736 a(2)3100 1705 y FA(])3125 1672 y Fs(d)3197 1705 y FA(of)31 b Fy(R)3361 1672 y Fs(d)3438 1705 y FA(and)g(a)118 1813 y(macroscopic)22 b(con\014guration)f(where)g(the)g(pure)g(phases)f(co)s(exist)i(is)e (describ)s(ed)g(b)m(y)h(a)h(function)e Fv(v)k FA(taking)118 1921 y(v)-5 b(alues)30 b Fu(f\006)p FA(1)p Fu(g)p FA(.)44 b(The)31 b(function)e Fv(v)35 b FA(should)29 b(b)s(e)h(in)m(terpreted)g (as)i(a)f(signed)f(indicator)g(represen)m(ting)g(the)118 2041 y(lo)s(cal)d(order)h(parameter)g(:)39 b(if)27 b Fv(v)1187 2055 y Fs(r)1251 2041 y FA(=)d(1)29 b(for)e(some)i Fv(r)e Fu(2)1944 2017 y Fq(b)1936 2041 y Fy(D)c FA(,)29 b(then)e(the)h(system)g(should)e(b)s(e)h(lo)s(cally)g(at)h Fv(r)j FA(in)118 2149 y(equilibrium)26 b(in)j(the)h(phase)g Fv(m)1196 2116 y Ft(\003)1196 2176 y Fs(\014)1243 2149 y FA(.)218 2266 y(T)-8 b(o)34 b(de\014ne)f(the)i(macroscopic)f(in)m (terfaces,)i(i.e.)51 b(the)34 b(b)s(oundary)e(of)i(the)h(set)f Fu(f)p Fv(v)h FA(=)c Fu(\000)p FA(1)p Fu(g)p FA(,)36 b(a)e(con)m(v)m(e-)118 2386 y(nien)m(t)e(functional)e(setting)i(is)g (the)g(space)g(BV)r(\()1751 2363 y Fq(b)1743 2386 y Fy(D)23 b Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))34 b(of)e(functions)f(of)h (b)s(ounded)e(v)-5 b(ariation)32 b(with)118 2506 y(v)-5 b(alues)42 b Fu(\006)p FA(1)g(in)684 2483 y Fq(b)677 2506 y Fy(D)65 b FA(and)41 b(uniformly)e(equal)j(to)h(1)g(outside)2195 2483 y Fq(b)2187 2506 y Fy(D)65 b FA(\(see)43 b([EG])g(for)f(a)g (review\).)76 b(F)-8 b(or)43 b(an)m(y)118 2626 y Fv(v)33 b Fu(2)d FA(BV)r(\()463 2603 y Fq(b)455 2626 y Fy(D)23 b Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))q(,)34 b(there)g(exists)f(a) g(generalized)g(notion)f(of)i(the)f(b)s(oundary)e(of)j(the)f(set)h Fu(f)p Fv(v)f FA(=)d Fu(\000)p FA(1)p Fu(g)118 2734 y FA(called)40 b(reduced)g(b)s(oundary)e(and)i(denoted)h(b)m(y)f Fv(@)1884 2701 y Ft(\003)1924 2734 y Fv(v)s FA(.)71 b(If)40 b Fu(f)p Fv(v)46 b FA(=)c Fu(\000)p FA(1)p Fu(g)f FA(is)f(a)h(regular)e (set,)44 b(then)c Fv(@)3574 2701 y Ft(\003)3614 2734 y Fv(v)118 2855 y FA(coincides)c(with)f(the)h(usual)f(b)s(oundary)g Fv(@)5 b(v)s FA(.)59 b(The)36 b(W)-8 b(ul\013)36 b(functional)f Fu(W)2695 2870 y Fs(\014)2778 2855 y FA(is)h(de\014ned)f(in)g Fy(L)3362 2869 y Fx(1)3407 2855 y FA(\()3450 2831 y Fq(b)3442 2855 y Fy(D)23 b FA(\))37 b(as)118 2962 y(follo)m(ws)693 3154 y Fu(W)783 3169 y Fs(\014)830 3154 y FA(\()p Fv(v)s FA(\))26 b(=)1069 3026 y Fq(\032)1179 3032 y(R)1222 3138 y Fs(@)1263 3119 y Fl(\003)1299 3138 y Fs(v)1355 3106 y Fv(\034)1395 3121 y Fs(\014)1442 3106 y FA(\()20 b Fv(~)-65 b(n)1532 3120 y Fs(x)1576 3106 y FA(\))15 b Fv(d)p Fu(H)1750 3120 y Fs(x)1794 3106 y Fv(;)197 b FA(if)97 b Fv(v)29 b Fu(2)c FA(BV)r(\()2503 3082 y Fq(b)2495 3106 y Fy(D)e Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))r Fv(;)1179 3214 y Fu(1)25 b Fv(;)743 b FA(otherwise)o Fv(:)3475 3154 y FA(\(2.4\))118 3389 y(T)-8 b(o)36 b(an)m(y)f(measurable)f (subset)h Fv(A)g FA(of)1416 3366 y Fq(b)1408 3389 y Fy(D)23 b FA(,)36 b(w)m(e)g(asso)s(ciate)g(the)f(function)f(1)-25 b(I)2636 3403 y Fs(A)2726 3389 y FA(=)33 b(1)2875 3403 y Fs(A)2928 3384 y Fp(c)2988 3389 y Fu(\000)23 b FA(1)3127 3403 y Fs(A)3219 3389 y FA(and)35 b(simply)118 3497 y(write)30 b Fu(W)441 3512 y Fs(\014)488 3497 y FA(\()p Fv(A)p FA(\))c(=)f Fu(W)838 3512 y Fs(\014)885 3497 y FA(\(1)-25 b(I)973 3511 y Fs(A)1030 3497 y FA(\).)218 3651 y(Let)31 b Fv(m)f FA(b)s(e)f(in)g(])21 b Fu(\000)f Fv(m)937 3618 y Ft(\003)937 3678 y Fs(\014)984 3651 y Fv(;)15 b(m)1104 3618 y Ft(\003)1104 3678 y Fs(\014)1151 3651 y FA([.)41 b(The)30 b(equilibrium)25 b(crystal)30 b(shap)s(es)g(are)g(the)h(solutions)e(of)h(the)h(W)-8 b(ul\013)118 3763 y(v)j(ariational)37 b(problem,)h(i.e.)62 b(they)38 b(are)g(the)g(minimizers)d(of)j(the)g(functional)e Fu(W)2946 3778 y Fs(\014)3030 3763 y FA(under)h(a)h(v)m(olume)118 3871 y(constrain)m(t)643 4056 y(min)810 3928 y Fq(\032)878 4056 y Fu(W)968 4071 y Fs(\014)1015 4056 y FA(\()p Fv(v)s FA(\))1163 3952 y Fq(\014)1163 4006 y(\014)1163 4061 y(\014)1224 4056 y Fv(v)28 b Fu(2)d FA(BV)r(\()1559 4033 y Fq(b)1551 4056 y Fy(D)e Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))r Fv(;)2122 3979 y Fq(\014)2122 4034 y(\014)2183 3933 y(Z)2238 4122 y Fk(b)2233 4139 y Fo(D)2300 4056 y Fv(m)2380 4019 y Ft(\003)2380 4080 y Fs(\014)2443 4056 y Fv(v)2487 4070 y Fs(r)2540 4056 y Fv(dr)2631 3979 y Fq(\014)2631 4034 y(\014)2686 4056 y Fr(6)25 b Fv(m)2862 3928 y Fq(\033)2945 4056 y Fv(:)505 b FA(\(2.5\))118 4265 y(Let)32 b Fu(D)352 4279 y Fs(m)449 4265 y FA(b)s(e)f(the)g(set)g (of)h(minimizers)c(of)38 b(\(2.5\))r(.)k(The)31 b(set)g(of)h(functions) d(of)i(b)s(ounded)e(p)s(erimeter)h(will)118 4373 y(also)g(pla)m(y)g(an) h(imp)s(ortan)m(t)e(role)h(in)f(the)i(follo)m(wing)e(:)40 b(for)30 b(an)m(y)h Fv(a)26 b(>)e FA(0,)31 b(w)m(e)g(set)884 4534 y Fu(C)932 4548 y Fs(a)999 4534 y FA(=)1095 4460 y Fq(\010)1148 4534 y Fv(v)d Fu(2)d FA(BV)r(\()1483 4510 y Fq(b)1475 4534 y Fy(D)e Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))27 b Fu(j)91 b(P)7 b FA(\()p Fu(f)p Fv(v)30 b FA(=)25 b Fu(\000)p FA(1)p Fu(g)p FA(\))h Fr(6)f Fv(a)2651 4460 y Fq(\011)2704 4534 y Fv(;)746 b FA(\(2.6\))118 4695 y(where)30 b Fu(P)38 b FA(denotes)31 b(the)f(p)s(erimeter.)40 b(This)28 b(set)j(is)f(compact)h(in)e(the)i Fy(L)2537 4662 y Fx(1)2612 4695 y FA(top)s(ology)-8 b(.)218 4856 y(The)23 b(microscopic)h(Ising)f(mo)s(del)g(is)g(em)m(b)s(edded)g(in)g (the)h(con)m(tin)m(uous)g(setting.)39 b(Let)3064 4833 y Fq(b)3056 4856 y Fy(D)3116 4870 y Fs(N)3214 4856 y FA(=)3334 4821 y Fx(1)p 3320 4836 64 4 v 3320 4888 a Fs(N)3393 4856 y Fy(Z)3458 4823 y Fs(d)3502 4856 y Fu(\\)3578 4833 y Fq(b)3571 4856 y Fy(D)22 b FA(.)118 4964 y(F)-8 b(or)24 b(simplicit)m(y)d(the)j(microscopic)f(size)g(is)g(c)m(hosen)h (in)e(the)i(binary)e(form)h Fv(N)35 b FA(=)25 b(2)2835 4931 y Fs(n)2906 4964 y FA(and)e(the)h(mesoscopic)118 5079 y(scale)38 b(is)f(denoted)g(b)m(y)h Fv(K)44 b FA(=)37 b(2)1200 5046 y Fs(k)1243 5079 y FA(.)62 b(The)37 b(cub)s(e)1754 5056 y Fq(b)1746 5079 y Fy(D)60 b FA(is)37 b(partionned)f(in)m(to)i(b)s (o)m(xes)2870 5056 y Fq(b)2865 5079 y Fy(B)2919 5093 y Fs(N)s(;K)3072 5079 y FA(,)i(eac)m(h)f(of)e(them)118 5204 y(con)m(taining)30 b Fv(K)644 5171 y Fs(d)715 5204 y FA(sites)g(of)1029 5180 y Fq(b)1021 5204 y Fy(D)1081 5218 y Fs(N)727 5427 y Fv(j)h Fu(2)25 b Fy(Z)946 5390 y Fs(d)982 5427 y Fv(;)45 b(x)26 b FA(=)f Fv(j)1278 5366 y(K)p 1278 5406 84 4 v 1278 5490 a(N)1397 5427 y Fu(2)1491 5404 y Fq(b)1483 5427 y Fy(D)1543 5441 y Fs(N)1616 5427 y Fv(;)1843 5404 y Fq(b)1838 5427 y Fy(B)1893 5441 y Fs(N)s(;K)2046 5427 y FA(\()p Fv(x)p FA(\))h(=)f Fv(x)20 b FA(+)2453 5299 y Fq(\025)2501 5427 y Fu(\000)2604 5366 y Fv(K)p 2582 5406 129 4 v 2582 5490 a FA(2)p Fv(N)2720 5427 y(;)2793 5366 y(K)p 2770 5406 V 2770 5490 a FA(2)p Fv(N)2909 5299 y Fq(\025)2957 5322 y Fs(d)3027 5427 y Fv(:)p eop %%Page: 6 6 6 5 bop 118 45 a Fx(6)1495 b(T.)23 b(BODINEA)n(U)118 373 y FA(Let)32 b Fy(B)337 387 y Fs(K)411 373 y FA(\()p Fv(N)10 b(x)p FA(\))32 b(b)s(e)f(the)h(microscopic)e(coun)m(terpart)i (of)2026 349 y Fq(b)2021 373 y Fy(B)2075 387 y Fs(N)t(;K)2229 373 y FA(\()p Fv(x)p FA(\),)g(i.e.)44 b(the)32 b(sites)f(of)3042 349 y Fq(b)3034 373 y Fy(D)3094 387 y Fs(N)3199 373 y FA(in)3311 349 y Fq(b)3306 373 y Fy(B)3360 387 y Fs(N)t(;K)3514 373 y FA(\()p Fv(x)p FA(\).)118 497 y(These)f(b)s(o)m(xes)h(are)g(cen)m (tered)g(on)f(the)h(sites)f(of)1742 474 y Fq(b)1734 497 y Fy(D)1794 511 y Fs(N)s(;K)1972 497 y FA(=)2078 461 y Fs(K)p 2078 476 65 4 v 2079 528 a(N)2152 497 y Fy(Z)2217 464 y Fs(d)2274 497 y Fu(\\)2362 474 y Fq(b)2354 497 y Fy(D)23 b FA(.)218 605 y(Finally)-8 b(,)45 b(the)f(lo)s(cal)f (magnetization)h(is)f(de\014ned)f(as)i(a)g(piece-wise)f(constan)m(t)i (function)e(on)g(the)118 720 y(partition)29 b Fu(f)547 697 y Fq(b)542 720 y Fy(B)597 734 y Fs(N)s(;K)750 720 y FA(\()p Fv(x)p FA(\))p Fu(g)947 915 y(8)p Fv(y)f Fu(2)1162 892 y Fq(b)1157 915 y Fy(B)1211 929 y Fs(N)t(;K)1365 915 y FA(\()p Fv(x)p FA(\))p Fv(;)197 b Fu(M)1818 929 y Fs(N)s(;K)1966 915 y FA(\()p Fv(y)s FA(\))26 b(=)2255 854 y(1)p 2215 895 125 4 v 2215 978 a Fv(K)2299 952 y Fs(d)2465 829 y Fq(X)2365 1030 y Fs(i)p Ft(2)p Fo(B)2474 1041 y Fp(K)2539 1030 y Fx(\()p Fs(N)7 b(x)p Fx(\))2712 915 y Fv(\033)2764 929 y Fs(i)2807 915 y Fv(:)643 b FA(\(2.7\))118 1168 y(The)30 b(lo)s(cal)g(order)g(parameter)g Fu(M)1301 1182 y Fs(N)s(;K)1479 1168 y FA(c)m(haracterizes)i(the)e(lo)s(cal)g (equilibrium.)118 1334 y(2.4.)47 b FF(Main)36 b(results.)46 b FA(The)31 b(follo)m(wing)e(results)i(describ)s(e)e(the)j(phenomenon)e (of)h(phase)g(co)s(existence)118 1442 y(with)41 b(di\013eren)m(t)g (accuracies.)77 b(The)41 b(system)i(is)e(analyzed)h(on)g(a)g(coarse)h (grained)f(lev)m(el)f(in)g(the)h Fy(L)3616 1409 y Fx(1)118 1550 y FA(top)s(ology)-8 b(.)218 1698 y(The)28 b(\014rst)h(result)f (implies)e(the)j(o)s(ccurrence)g(of)g(phase)g(segregation)h(\(in)e(a)i (w)m(eak)g(form\),)f(i.e.)40 b(with-)118 1806 y(out)h(describing)d (explicitly)h(the)i(limiting)c(crystal)k(shap)s(es.)71 b(This)39 b(should)f(b)s(e)i(in)m(terpreted)g(as)h(an)118 1914 y(in)m(termediate)i(step)g(on)g(the)g(w)m(a)m(y)h(to)g(the)g(W)-8 b(ul\013)42 b(construction.)79 b(Let)43 b Fj(B)h FA(b)s(e)e(the)i(set)f (of)g(in)m(v)m(erse)118 2022 y(temp)s(eratures)36 b(for)g(whic)m(h)e (the)j(P)m(eierls)e(estimate)i(holds)d(:)52 b(for)36 b(an)m(y)g Fv(\014)42 b FA(in)34 b Fj(B)p FA(,)k(there)f(is)e(a)h (constan)m(t)118 2129 y Fv(c)157 2144 y Fs(\014)230 2129 y Fv(>)25 b(C)7 b FA(\()p Fv(d)p FA(\))28 b(\(where)h Fv(C)7 b FA(\()p Fv(d)p FA(\))28 b(is)f(a)i(constan)m(t)g(large)g (enough)f(dep)s(ending)d(on)k(the)f(dimension\))e(suc)m(h)i(that)118 2237 y(an)m(y)j(spin)d(con)m(tour)j(\000)f(of)h(length)f Fu(j)p FA(\000)p Fu(j)g FA(has)g(exp)s(onen)m(tially)f(small)g (probabilit)m(y)f(\(uniformly)g(in)h Fv(N)10 b FA(\))1322 2387 y Fv(\026)1377 2349 y Fx(+)1377 2416 y Fs(\014)s(;N)1507 2313 y Fq(\000)1548 2387 y FA(\000\))26 b Fr(6)40 b FA(exp\()p Fu(\000)p Fv(c)2061 2402 y Fs(\014)2108 2387 y Fu(j)p FA(\000)p Fu(j)p FA(\))15 b Fv(:)1185 b FA(\(2.8\))118 2540 y(F)-8 b(urthermore,)31 b Fv(c)710 2555 y Fs(\014)787 2540 y FA(div)m(erges)g(as)f Fv(\014)36 b FA(go)s(es)31 b(to)g(in\014nit)m(y)-8 b(.)118 2704 y FF(Theorem)31 b(2.2.)39 b Fn(L)-5 b(et)31 b Fv(\014)k Fn(b)-5 b(e)30 b(in)g Fu(B)i Fn(and)f Fv(m)e Fn(b)-5 b(e)30 b(in)g FA(])14 b Fu(\000)g Fv(m)2016 2671 y Ft(\003)2016 2731 y Fs(\014)2064 2704 y Fv(;)h(m)2184 2671 y Ft(\003)2184 2731 y Fs(\014)2231 2704 y FA([)p Fn(.)41 b(Ther)-5 b(e)31 b(is)f Fv(a)25 b(>)g FA(0)31 b Fn(such)f(that)h(for)f(every)118 2821 y Fv(\016)f(>)c FA(0)p Fn(,)33 b(ther)-5 b(e)34 b(is)e(a)h(sc)-5 b(ale)33 b Fv(K)1087 2835 y Fx(0)1152 2821 y FA(=)25 b Fv(K)1325 2835 y Fx(0)1365 2821 y FA(\()p Fv(\014)5 b(;)15 b(\016)s FA(\))35 b Fn(and)378 3051 y Fu(8)p Fv(K)d Fr(>)25 b Fv(K)711 3065 y Fx(0)750 3051 y Fv(;)426 b FA(lim)1162 3111 y Fs(N)7 b Ft(!1)1407 3051 y Fv(\026)1462 3013 y Fx(+)1462 3080 y Fs(\014)s(;N)1607 2895 y Fq( )1729 2989 y FA(1)p 1689 3030 127 4 v 1689 3113 a Fv(m)1769 3082 y Ft(\003)1769 3143 y Fs(\014)1826 3051 y Fu(M)1935 3065 y Fs(N)s(;K)2107 3051 y Fu(2)25 b(V)7 b FA(\()p Fu(C)2339 3065 y Fs(a)2381 3051 y Fv(;)15 b(\016)s FA(\))2533 2946 y Fq(\014)2533 3001 y(\014)2533 3055 y(\014)2589 3051 y FF(M)2688 3065 y Fs(N)2780 3051 y Fr(6)25 b Fv(m)2956 2895 y Fq(!)3053 3051 y FA(=)g(1)15 b Fv(;)118 3289 y Fn(wher)-5 b(e)34 b Fu(C)423 3303 y Fs(a)497 3289 y Fn(has)f(b)-5 b(e)g(en)33 b(de\014ne)-5 b(d)34 b(in)39 b FA(\(2.6\))c Fn(and)e Fu(V)7 b FA(\()p Fu(C)1826 3303 y Fs(a)1868 3289 y Fv(;)15 b(\016)s FA(\))35 b Fn(is)d(the)h Fv(\016)s Fn(-neighb)-5 b(orho)g(o)g(d)37 b(of)c Fu(C)3041 3303 y Fs(a)3115 3289 y Fn(in)f Fy(L)3281 3256 y Fx(1)787 3464 y Fu(V)7 b FA(\()p Fu(C)933 3478 y Fs(a)975 3464 y Fv(;)15 b(\016)s FA(\))26 b(=)1215 3363 y Fq(n)1276 3464 y Fv(v)j Fu(2)24 b Fy(L)1489 3427 y Fx(1)1535 3391 y Fq(\000)1584 3441 y(b)1576 3464 y Fy(D)1642 3391 y Fq(\001)1716 3387 y(\014)1716 3441 y(\014)1746 3464 y Fu(9)p Fv(v)1844 3427 y Ft(0)1893 3464 y Fu(2)h(C)2027 3478 y Fs(a)2068 3464 y Fv(;)108 b Fu(k)p Fv(v)24 b Fu(\000)c Fv(v)2452 3427 y Ft(0)2476 3464 y Fu(k)2521 3478 y Fx(1)2586 3464 y Fr(6)25 b Fv(\016)2725 3363 y Fq(o)2802 3464 y Fv(:)218 3650 y FA(This)g(result)g(implies)g(that)i(on)g(a)g (macroscopic)g(scale,)h(one)f(observ)m(es)h(macroscopic)f(droplets)f (with)118 3758 y(phase)36 b(b)s(oundaries)d(of)k(p)s(erimeter)e (smaller)f(than)i Fv(a)p FA(.)58 b(The)35 b(pro)s(of)h(of)g(Theorem)g (2.2)h(is)e(based)h(on)g(a)118 3866 y(general)31 b(approac)m(h)h(dev)m (elop)s(ed)e(in)g([BIV1)q(])i(and)e(on)h(a)h(new)e(coarse)j(graining.) 41 b(Notice)32 b(that)g(for)f(Kac)118 3974 y(Ising)e(mo)s(dels,)h(a)g (similar)e(result)h(w)m(as)i(already)f(deriv)m(ed)g(in)f([BBP)q(].)218 4082 y(The)j(argumen)m(t,)i(implemen)m(ted)d(in)g(this)g(pap)s(er)h (for)g(the)h(nearest)g(neigh)m(b)s(or)e(Ising)h(mo)s(del)f(at)j(lo)m(w) 118 4190 y(temp)s(erature,)29 b(is)e(robust)g(and)h(should)e(also)i (apply)f(to)i(mo)s(dels)e(in)g(the)h(Pirogo)m(v)h(Sinai)d(Theory)h(\(p) s(os-)118 4298 y(sibly)h(con)m(taining)i(sev)m(eral)h(phases\).)41 b(This)28 b(rough)i(description)e(relies)h(on)i(P)m(eierls)e(t)m(yp)s (e)i(estimates.)218 4405 y(Another)k(c)m(haracterization)h(of)f(phase)g (segregation)h(is)e(the)h(o)s(ccurrence)g(of)g(surface)g(order)f(large) 118 4513 y(deviations)29 b(\(see)j([Sc,)e(Pi]\).)41 b(This)28 b(is)i(a)h(direct)e(consequence)j(of)e(the)h(pro)s(of)e(of)i(Theorem)f (2.2.)118 4677 y FF(Corollary)36 b(2.1.)42 b Fn(L)-5 b(et)33 b Fv(\014)38 b Fn(b)-5 b(e)32 b(in)g Fu(B)j Fn(and)f Fv(m)e Fn(in)g FA(])20 b Fu(\000)g Fv(m)1967 4644 y Ft(\003)1967 4704 y Fs(\014)2014 4677 y Fv(;)15 b(m)2134 4644 y Ft(\003)2134 4704 y Fs(\014)2181 4677 y FA([)p Fn(.)42 b(Then,)33 b(ther)-5 b(e)33 b(exists)g Fv(c)3055 4692 y Fs(\014)3128 4677 y Fv(>)25 b FA(0)32 b Fn(such)h(that)951 4886 y FA(lim)15 b(sup)988 4964 y Fs(N)7 b Ft(!1)1363 4824 y FA(1)p 1279 4865 214 4 v 1279 4948 a Fv(N)1362 4922 y Fs(d)p Ft(\000)p Fx(1)1518 4886 y FA(log)17 b Fv(\026)1706 4847 y Fx(+)1706 4915 y Fs(\014)s(;N)1850 4886 y FA(\()q FF(M)1985 4900 y Fs(N)2077 4886 y Fr(6)25 b Fv(m)p FA(\))41 b Fr(6)k Fu(\000)20 b Fv(c)2575 4901 y Fs(\014)2638 4886 y Fv(:)218 5140 y FA(The)i(computation)h(of)g(sharp)f(asymptotic)h (with)e(the)i(exact)i(surface)e(tension)f(factor)i(enables)e(to)i(go) 118 5247 y(b)s(ey)m(ond)i(the)h(previous)f(result)f(and)i(to)g(pro)m(v) m(e)h(the)f Fy(L)1921 5214 y Fx(1)1994 5247 y FA(concen)m(tration)g(of) g(the)g(lo)s(cal)g(order)f(parameter)118 5355 y Fu(M)227 5369 y Fs(N)s(;K)407 5355 y FA(to)33 b(the)f(minimizers)d(of)k(the)f(v) -5 b(ariational)31 b(problem)g(\(2.5\))r(.)46 b(Let)33 b(us)f(state)h(the)g(result)e(for)h(the)118 5469 y(Kac)c(Ising)e(mo)s (del.)39 b(F)-8 b(or)28 b(a)g(giv)m(en)g(range)g(of)f(the)h(in)m (teractions)2294 5433 y Fx(1)p 2291 5448 41 4 v 2291 5501 a Fs(\015)2341 5469 y FA(,)h(the)e(magnetization)h(is)f(denoted)g (b)m(y)p eop %%Page: 7 7 7 6 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)782 b(7)118 366 y Fv(m)198 333 y Ft(\003)198 394 y Fs(\014)s(;\015)336 366 y FA(\(2.3\))r(,)31 b(the)h(surface)f (tension)f(b)m(y)h Fv(\034)1525 381 y Fs(\014)s(;\015)1663 366 y FA(\(2.2\))i(and)d(the)i(set)f(of)h(the)f(equilibrium)26 b(crystal)31 b(shap)s(es)118 484 y Fu(D)188 498 y Fs(m;\015)345 484 y FA(\(2.5\))r(.)118 646 y FF(Theorem)41 b(2.3.)46 b Fn(F)-7 b(or)39 b(any)g Fv(\014)i(>)35 b FA(1)p Fn(,)40 b(let)e(us)h(\014x)f Fv(\015)j Fu(2)p FA(]0)p Fv(;)15 b(\015)2138 661 y Fs(\014)2186 646 y FA([)38 b Fn(and)h Fv(m)d Fu(2)p FA(])24 b Fu(\000)g Fv(m)2832 613 y Ft(\003)2832 674 y Fs(\014)s(;\015)2939 646 y Fv(;)15 b(m)3059 613 y Ft(\003)3059 674 y Fs(\014)s(;\015)3166 646 y FA([)p Fn(.)59 b(F)-7 b(or)39 b(every)118 763 y Fv(\016)29 b(>)c FA(0)p Fn(,)33 b(one)g(c)-5 b(an)33 b(cho)-5 b(ose)34 b(a)f(sc)-5 b(ale)34 b Fv(K)1391 777 y Fx(0)1456 763 y FA(=)25 b Fv(K)1629 777 y Fx(0)1668 763 y FA(\()p Fv(\014)5 b(;)15 b(\015)5 b(;)15 b(\016)s FA(\))35 b Fn(such)e(that)h(for)f(any)g Fv(K)f Fr(>)25 b Fv(K)2998 777 y Fx(0)613 965 y FA(lim)574 1025 y Fs(N)7 b Ft(!1)819 965 y Fv(\026)874 901 y Fs(m)936 877 y Fl(\003)936 924 y Fp(\014)874 994 y Fs(\014)s(;\015)t(;N)1079 837 y Fq(\022)1216 965 y FA(inf)1146 1025 y Fs(v)r Ft(2D)1284 1033 y Fp(m;\015)1412 965 y Fu(kM)1566 979 y Fs(N)s(;K)1734 965 y Fu(\000)20 b Fv(m)1905 927 y Ft(\003)1905 988 y Fs(\014)s(;\015)2012 965 y Fv(v)s Fu(k)2104 979 y Fx(1)2170 965 y Fr(6)25 b Fv(\016)2342 860 y Fq(\014)2342 915 y(\014)2342 969 y(\014)2398 965 y FF(M)2497 979 y Fs(N)2589 965 y Fr(6)g Fv(m)2765 837 y Fq(\023)2857 965 y FA(=)g(1)15 b Fv(:)218 1179 y FA(The)37 b(con)m(v)m(ergence)j(of)e(the)f(surface)h (tension)f Fv(\034)1871 1194 y Fs(\014)s(;\015)2015 1179 y FA(to)h(the)g(anisotropic)f(v)-5 b(an)37 b(der)g(W)-8 b(aals)38 b(surface)118 1286 y(tension)30 b(w)m(as)h(pro)m(v)m(en)f(in) g([BBBP)q(].)41 b(This)29 b(implies)e(that)k(the)g(equilibrium)26 b(crystal)k(shap)s(es)f(con)m(v)m(erge)118 1394 y(to)44 b(spheres)e(as)h Fv(\015)48 b FA(v)-5 b(anishes)41 b(\(when)i(the)g (equilibrium)38 b(crystal)43 b(shap)s(es)f(are)h(giv)m(en)g(b)m(y)g (the)g(W)-8 b(ul\013)118 1502 y(construction,)30 b(i.e.)41 b(for)30 b(v)-5 b(alues)30 b(of)g Fv(m)g FA(close)h(enough)f(to)h Fv(m)2166 1469 y Ft(\003)2166 1530 y Fs(\014)2213 1502 y FA(\).)118 1674 y FF(Remark)37 b(2.1.)44 b Fn(In)35 b(a)g(gr)-5 b(oundbr)g(e)g(aking)37 b(work)e(L)-5 b(eb)g(owitz,)37 b(Mazel,)e(Pr)-5 b(esutti)36 b FA([LMP])f Fn(pr)-5 b(ove)g(d)37 b(the)e(liq-)118 1782 y(uid/vap)-5 b(or)34 b(tr)-5 b(ansition)33 b(for)e(p)-5 b(articles)33 b(in)e(the)g(c)-5 b(ontinuum)32 b(inter)-5 b(acting)32 b(with)g(Kac)f(p)-5 b(otentials.)44 b(Their)118 1890 y(pr)-5 b(o)g(of)32 b(is)d(b)-5 b(ase)g(d)31 b(on)f(a)g(r)-5 b(enormalization)33 b(pr)-5 b(o)g(c)g(e)g(dur)g(e)33 b(which)e(enables)e(to)i(r)-5 b(e)g(duc)g(e)30 b(the)g(system)g(to)h(c) -5 b(o)g(arse)118 1998 y(gr)g(aine)g(d)29 b(variables)g(with)g(pr)-5 b(op)g(erties)30 b(similar)g(to)e(the)g(ones)h(of)f(the)g(c)-5 b(o)g(arse)30 b(gr)-5 b(aine)g(d)29 b(Kac)f(Ising)g(mo)-5 b(del.)118 2106 y(Ther)g(efor)g(e,)28 b(it)d(is)f(natur)-5 b(al)27 b(to)e(hop)-5 b(e)26 b(that)g(p)-5 b(arts)27 b(of)d(the)i(ar)-5 b(gument)25 b(develop)-5 b(e)g(d)27 b(for)e(the)g(Kac)g(Ising)g(mo)-5 b(del)118 2214 y(c)g(ould)36 b(b)-5 b(e)35 b(tr)-5 b(ansp)g(ose)g(d)39 b(in)c(the)h(fr)-5 b(amework)37 b(investigate)-5 b(d)37 b(in)e FA([LMP])p Fn(.)50 b(F)-7 b(or)36 b(the)g(moment)g(the)g(lack)f(of)118 2322 y(ferr)-5 b(omagnetic)39 b(ine)-5 b(qualities)37 b(and)i(of)e(symmetry)i(b)-5 b(etwe)g(en)37 b(the)h(phases)h(ar)-5 b(e)38 b(major)g(di\016culties)g(for)118 2429 y(the)i(analysis)h(of)f (surfac)-5 b(e)40 b(tension.)64 b(These)40 b(pr)-5 b(oblems)41 b(ar)-5 b(e)41 b(also)f(enc)-5 b(ounter)g(e)g(d)42 b(for)e(the)g (derivation)118 2537 y(of)35 b(surfac)-5 b(e)35 b(tension)g(in)g(the)g (Pir)-5 b(o)g(gov)35 b(Sinai)g(The)-5 b(ory.)50 b(Nevertheless,)35 b(the)g(b)-5 b(asic)35 b(phase)g(se)-5 b(gr)g(e)g(gation)118 2645 y(phenomenon)44 b(\(se)-5 b(e)43 b(The)-5 b(or)g(em)44 b(2.2\))f(fol)5 b(lows)44 b(in)e(this)h(c)-5 b(ontext)43 b(fr)-5 b(om)43 b(the)g(ar)-5 b(gument)43 b(develop)-5 b(e)g(d)44 b(in)118 2753 y FA([BBP)q(])p Fn(.)118 2916 y FF(Remark)i(2.2.)i Fn(The)-5 b(or)g(em)44 b(2.2)f(c)-5 b(ould)43 b(also)g(have)g(b)-5 b(e)g(en)42 b(state)-5 b(d)44 b(for)e(di\013er)-5 b(ent)43 b(typ)-5 b(es)43 b(of)f(b)-5 b(oundary)118 3024 y(c)g(onditions)35 b(\(fr)-5 b(e)g(e,)33 b(mixe)-5 b(d,)33 b(...\).)1497 3210 y FA(3.)46 b Fz(The)35 b Fy(L)1880 3177 y Fx(1)1960 3210 y Fz(theor)-6 b(y)218 3372 y FA(In)25 b(this)h(section,)h(the)g(salien)m(t)e (features)i(of)f(the)h(pro)s(of)f(are)g(outlined.)38 b(F)-8 b(or)27 b(simplicit)m(y)-8 b(,)25 b(w)m(e)i(fo)s(cus)e(on)118 3480 y(the)36 b(Ising)e(mo)s(del)g(with)g(nearest)h(neigh)m(b)s(or)f (in)m(teraction)h(at)h(lo)m(w)f(temp)s(erature)g(and)g(p)s(ostp)s(one)f (the)118 3588 y(study)29 b(of)h(Kac)h(Ising)e(mo)s(del)g(to)i(section)f (4.)41 b(The)29 b(basic)h(assumption)e(is)h(the)h(v)-5 b(alidit)m(y)29 b(of)h(the)g(P)m(eierls)118 3696 y(estimate)h(\(2.8\))r (.)118 3860 y(3.1.)47 b FF(Phase)40 b(segregation.)46 b FA(Theorem)35 b(2.2)g(and)f(corollary)g(2.1)i(are)f(direct)f (consequences)h(of)g(the)118 3968 y(follo)m(wing)29 b(exp)s(onen)m (tial)g(tigh)m(tness)i(theorem.)118 4130 y FF(Prop)s(osition)j(3.1.)40 b Fn(L)-5 b(et)31 b Fv(\014)36 b Fn(b)-5 b(e)30 b(in)h Fj(B)p Fn(.)41 b(Then)31 b(ther)-5 b(e)31 b(exists)g(a)g(c)-5 b(onstant)33 b Fv(C)7 b FA(\()p Fv(\014)e FA(\))25 b Fv(>)g FA(0)31 b Fn(such)g(that)h(for)f(al)5 b(l)118 4238 y Fv(\016)36 b Fn(p)-5 b(ositive)34 b(one)f(c)-5 b(an)33 b(\014nd)g Fv(K)1119 4252 y Fx(0)1159 4238 y FA(\()p Fv(\016)s FA(\))h Fn(such)f(that)h(for)f Fv(K)f Fr(>)25 b Fv(K)2126 4252 y Fx(0)361 4467 y Fu(8)p Fv(a)g(>)g FA(0)p Fv(;)202 b FA(lim)15 b(sup)890 4546 y Fs(N)7 b Ft(!1)1265 4406 y FA(1)p 1181 4446 214 4 v 1181 4530 a Fv(N)1264 4504 y Fs(d)p Ft(\000)p Fx(1)1420 4467 y FA(log)16 b Fv(\026)1607 4429 y Fx(+)1607 4497 y Fs(\014)s(;N)1752 4312 y Fq( )1875 4406 y FA(1)p 1834 4446 127 4 v 1834 4530 a Fv(m)1914 4498 y Ft(\003)1914 4559 y Fs(\014)1971 4467 y Fu(M)2080 4481 y Fs(N)s(;K)2253 4467 y Fu(62)25 b(V)7 b FA(\()p Fu(C)2485 4481 y Fs(a)2527 4467 y Fv(;)15 b(\016)s FA(\))2645 4312 y Fq(!)2759 4467 y Fr(6)45 b Fu(\000)20 b Fv(C)7 b FA(\()p Fv(\014)e FA(\))15 b Fv(a;)118 4717 y Fn(wher)-5 b(e)34 b Fu(V)7 b FA(\()p Fu(C)521 4731 y Fs(a)563 4717 y Fv(;)15 b(\016)s FA(\))34 b Fn(is)f(the)g Fv(\016)s Fn(-neighb)-5 b(orho)g(o)g(d)36 b(of)d Fu(C)1735 4731 y Fs(a)1809 4717 y Fn(in)f Fy(L)1975 4684 y Fx(1)2021 4717 y FA(\()2064 4694 y Fq(b)2056 4717 y Fy(D)23 b FA(\))p Fn(.)218 4880 y FA(This)30 b(prop)s(osition)f(tells)i(us)g(that)h(only) f(the)h(con\014gurations)f(close)h(to)h(the)f(compact)h(set)f Fu(C)3409 4894 y Fs(a)3482 4880 y FA(ha)m(v)m(e)118 4988 y(a)f(con)m(tribution)e(whic)m(h)g(is)g(of)i(a)g(surface)f(order.)218 5135 y(Let)f(us)e(\014rst)h(deduce)g(Theorem)g(2.2)h(and)f(Corollary)f (2.1)i(from)f(Prop)s(osition)e(3.1.)41 b(There)28 b(exists)g(a)118 5243 y(constan)m(t)k Fv(c)524 5258 y Fs(d)595 5243 y FA(dep)s(ending)c(on)i(the)h(dimension)c(suc)m(h)j(that)402 5370 y(1)p 365 5410 120 4 v 365 5493 a Fv(m)445 5467 y Ft(\003)495 5431 y Fu(M)604 5445 y Fs(N)s(;K)776 5431 y Fu(2)25 b(V)7 b FA(\()p Fu(C)1008 5445 y Fs(a)1050 5431 y Fv(;)15 b(\016)s FA(\))27 b Fu(\))e FF(M)1410 5445 y Fs(N)1503 5431 y FA(=)1599 5307 y Fq(Z)1654 5496 y Fk(b)1649 5514 y Fo(D)1717 5431 y Fu(M)1826 5445 y Fs(N)s(;K)1973 5431 y FA(\()p Fv(x)p FA(\))15 b Fv(dx)26 b Fr(>)f Fv(m)2411 5394 y Ft(\003)2450 5431 y FA(\(1)c Fu(\000)f Fv(\016)k Fu(\000)c Fv(c)2836 5446 y Fs(d)2877 5431 y Fv(a)2925 5394 y Fs(d=)p Fx(\()p Fs(d)p Ft(\000)p Fx(1\))3182 5431 y FA(\))15 b Fv(:)p eop %%Page: 8 8 8 7 bop 118 45 a Fx(8)1495 b(T.)23 b(BODINEA)n(U)118 366 y FA(Therefore)f(the)g(spin)e(con\014gurations)i(in)e Fu(f)p FF(M)1674 380 y Fs(N)1767 366 y Fr(6)25 b Fv(m)p Fu(g)e FA(for)e Fv(m)26 b(<)f(m)2423 333 y Ft(\003)2484 366 y FA(b)s(elong)c(as)h(w)m(ell)f(to)3148 293 y Fq(\010)3242 331 y Fx(1)p 3211 346 99 4 v 3211 398 a Fs(m)3273 379 y Fl(\003)3319 366 y Fu(M)3428 380 y Fs(N)s(;K)3601 366 y Fu(62)118 484 y(V)7 b FA(\()p Fu(C)264 498 y Fs(a)306 484 y Fv(;)15 b(\016)s FA(\))424 410 y Fq(\011)506 484 y FA(for)27 b(some)h Fv(a)d(>)g FA(0)i(and)g Fv(\016)i(>)c FA(0.)40 b(An)27 b(application)e(of)j(Prop)s(osition)d(3.1)j(leads)f (to)h(the)f(surface)118 592 y(order)j(deviations)f(of)i(Corollary)e (2.1.)218 700 y(T)-8 b(o)31 b(pro)m(v)m(e)g(Theorem)f(2.2)h(it)f(is)g (enough)g(to)h(c)m(hec)m(k)h(that)f(there)f(is)g(a)h(constan)m(t)g Fv(c)2981 714 y Fx(0)3051 700 y FA(suc)m(h)f(that)968 886 y(lim)15 b(inf)991 947 y Fs(N)7 b Ft(!1)1354 825 y FA(1)p 1270 865 214 4 v 1270 948 a Fv(N)1353 922 y Fs(d)p Ft(\000)p Fx(1)1509 886 y FA(log)16 b Fv(\026)1696 848 y Fx(+)1696 915 y Fs(\014)s(;N)1841 886 y FA(\()p FF(M)1975 900 y Fs(N)2068 886 y Fr(6)25 b Fv(m)p FA(\))41 b Fr(>)k Fu(\000)20 b Fv(c)2566 900 y Fx(0)2621 886 y Fv(:)118 1067 y FA(This)31 b(follo)m(ws)h(from)h(the)g(P)m(eierls)f (estimate)h(and)g(the)g(exp)s(onen)m(tial)f(relaxation)g(in)g(the)h (pure)f(phases)118 1175 y(\(for)f Fv(\014)f Fu(2)25 b Fj(B)p FA(\).)218 1323 y(The)41 b(deriv)-5 b(ation)40 b(of)i(Prop)s(osition)e(3.1)j(is)e(based)g(up)s(on)f(a)j(coarse)g (grained)d(description)g(of)i(the)118 1431 y(system)37 b(and)e(a)i(theorem)g(\(v)-5 b(alid)35 b(for)h(general)h(coarse)g (graining\))e(whic)m(h)g(ensures)h(the)g(exp)s(onen)m(tial)118 1539 y(tigh)m(tness)30 b(\(see)i([BIV1)q(]\).)118 1687 y Fn(Co)-5 b(arse)34 b(gr)-5 b(aining)34 b(:)p 118 1720 686 4 v 218 1800 a FA(This)42 b(coarse)j(grained)e(description)f(is)h (obtained)h(under)e(the)i(P)m(eierls)f(condition)g(\(2.8\))r(.)81 b(It)44 b(is)118 1908 y(v)-5 b(alid)36 b(in)h(an)m(y)h(dimensions)d Fv(d)i Fr(>)h FA(2)g(and)f(do)s(es)g(not)h(require)e(correlations)i (inequalities)d(or)i(the)h(FK)118 2016 y(represen)m(tation.)218 2123 y(The)26 b(t)m(ypical)h(spin)e(con\014gurations)i(are)h(de\014ned) e(at)h(the)h(mesoscopic)f(scale)h Fv(K)k FA(=)25 b(2)3116 2090 y Fs(k)3159 2123 y FA(.)39 b(Let)28 b Fv(@)5 b Fy(B)3491 2137 y Fs(K)3591 2123 y FA(=)118 2231 y Fy(B)173 2245 y Fs(K)g Fx(+)p Fs(K)358 2227 y Fp(\013)431 2231 y Fu(n)21 b Fy(B)551 2245 y Fs(K)657 2231 y FA(b)s(e)30 b(the)h(enlarged)f (external)h(b)s(oundary)e(of)i(the)g(b)s(o)m(x)g Fy(B)2554 2245 y Fs(K)2629 2231 y FA(,)g(where)f Fv(\013)h FA(is)f(in)g(\(0)p Fv(;)15 b FA(1\).)44 b(The)118 2339 y(parameter)31 b Fv(\020)h(>)25 b FA(0)30 b(will)e(con)m(trol)j(the)f(accuracy)i(of)f (the)f(coarse)i(graining.)218 2454 y(Let)f Fv(x)g FA(b)s(e)f(in)702 2431 y Fq(b)694 2454 y Fy(D)754 2468 y Fs(N)s(;K)907 2454 y FA(.)42 b(F)-8 b(or)32 b(an)m(y)f Fv(")26 b FA(=)g Fu(\006)p FA(1,)31 b(the)g(b)s(o)m(x)1984 2431 y Fq(b)1979 2454 y Fy(B)2034 2468 y Fs(N)s(;K)2187 2454 y FA(\()p Fv(x)p FA(\))g(is)f Fv(")p FA(-)p Fn(go)-5 b(o)g(d)33 b FA(if)d(the)h(spin)e(con\014guration)118 2562 y(inside)f(the)j (enlarged)f(b)s(o)m(x)g Fy(B)1125 2576 y Fs(K)5 b Fx(+)p Fs(K)1310 2558 y Fp(\013)1363 2562 y FA(\()p Fv(x)p FA(\))31 b(is)f(t)m(ypical,)g(i.e.)118 2778 y FF(\(P1\))37 b FA(The)f(b)s(o)m(x) h Fy(B)789 2792 y Fs(K)863 2778 y FA(\()p Fv(x)p FA(\))h(is)e (surrounded)e(b)m(y)j(at)h(least)f(a)g(connected)h(surface)f(of)g (spins)e(in)g Fv(@)5 b Fy(B)3464 2792 y Fs(K)3539 2778 y FA(\()p Fv(x)p FA(\))118 2886 y(with)29 b(sign)h(uniformly)d(equal)j (to)h Fv(")p FA(.)118 2994 y FF(\(P2\))f FA(The)f(a)m(v)m(erage)j (magnetization)e Fu(M)1563 3008 y Fs(N)s(;K)1711 2994 y FA(\()p Fv(x)p FA(\))g(inside)d Fy(B)2175 3008 y Fs(K)2249 2994 y FA(\()p Fv(x)p FA(\))j(is)f(close)h(to)g(the)g(equilibrium)25 b(v)-5 b(alue)118 3102 y Fv("m)240 3069 y Ft(\003)1430 3135 y Fq(\014)1430 3190 y(\014)1460 3212 y Fu(M)1569 3226 y Fs(N)s(;K)1716 3212 y FA(\()p Fv(x)p FA(\))21 b Fu(\000)f Fv("m)2072 3175 y Ft(\003)2112 3135 y Fq(\014)2112 3190 y(\014)2167 3212 y Fr(6)25 b Fv(\020)d(:)1125 b FA(\(3.1\))218 3403 y(On)29 b(the)i(mesoscopic)f(lev)m(el,)h(eac)m(h)g (b)s(o)m(x)1608 3380 y Fq(b)1603 3403 y Fy(B)1657 3417 y Fs(N)s(;K)1810 3403 y FA(\()p Fv(x)p FA(\))g(is)f(lab)s(elled)e(b)m (y)i(a)h(mesoscopic)f(phase)g(lab)s(el)713 3638 y Fu(8)p Fv(x)25 b Fu(2)934 3614 y Fq(b)926 3638 y Fy(D)986 3652 y Fs(N)s(;K)1139 3638 y Fv(;)197 b(u)1413 3593 y Fs(\020)1413 3666 y(N)s(;K)1561 3638 y FA(\()p Fv(x)p FA(\))25 b(=)1804 3482 y Fq(\()1878 3576 y Fv(";)276 b FA(if)2310 3553 y Fq(b)2304 3576 y Fy(B)2359 3590 y Fs(N)s(;K)2512 3576 y FA(\()p Fv(x)p FA(\))31 b(is)f Fv(")p FA(-)p Fn(go)-5 b(o)g(d)32 b Fv(;)1878 3706 y FA(0)p Fv(;)273 b FA(otherwise)p Fv(:)118 3913 y 16222704 9323399 0 0 44139560 25260195 startTexFig 118 3913 a %%BeginDocument: ./pictures/coarse.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: coarse.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Tue Aug 8 19:41:29 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 671 384 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 384 moveto 0 0 lineto 671 0 lineto 671 384 lineto closepath clip newpath % Fill background color 0 0 moveto 671 0 lineto 671 384 lineto 0 384 lineto closepath 1.00 1.00 1.00 setrgbcolor fill -60.0 444.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline 30.000 slw n 1200 1200 m 7200 1200 l 7200 7200 l 1200 7200 l cp gs col0 s gr % Polyline 7.500 slw [60 30 15 30] 0 sd n 6600 1800 m 11400 1800 l 11400 6600 l 6600 6600 l cp gs col0 s gr [] 0 sd % Polyline gs clippath 9240 6465 m 9360 6465 l 9360 6210 l 9300 6435 l 9240 6210 l cp 9360 1935 m 9240 1935 l 9240 2190 l 9300 1965 l 9360 2190 l cp eoclip n 9300 1950 m 9300 6450 l gs col0 s gr gr % arrowhead n 9360 2190 m 9300 1965 l 9240 2190 l 9300 2145 l 9360 2190 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 9240 6210 m 9300 6435 l 9360 6210 l 9300 6255 l 9240 6210 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9277 7065 m 9322 7065 l 9322 6939 l 9300 7033 l 9277 6939 l cp 9322 6660 m 9277 6660 l 9277 6785 l 9300 6692 l 9322 6785 l cp eoclip n 9300 6675 m 9300 7050 l gs col0 s gr gr % arrowhead n 9322 6785 m 9300 6692 l 9277 6785 l 9300 6767 l 9322 6785 l cp gs 0.00 setgray ef gr col0 s % arrowhead n 9277 6939 m 9300 7033 l 9322 6939 l 9300 6958 l 9277 6939 l cp gs 0.00 setgray ef gr col0 s % Polyline n 1800 1800 m 6600 1800 l 6600 6600 l 1800 6600 l cp gs col7 0.90 shd ef gr gs col0 s gr % Polyline 60.000 slw n 1650 1575 m 1632 1575 l 1620 1574 l 1612 1571 l 1606 1569 l 1601 1566 l 1595 1566 l 1585 1568 l 1575 1575 l 1568 1585 l 1566 1595 l 1566 1601 l 1569 1606 l 1571 1612 l 1574 1620 l 1575 1632 l 1575 1650 l 1575 1667 l 1575 1679 l 1575 1685 l 1575 1688 l 1575 1690 l 1575 1696 l 1575 1708 l 1575 1725 l 1575 1743 l 1574 1755 l 1571 1763 l 1569 1769 l 1566 1774 l 1566 1780 l 1568 1790 l 1575 1800 l 1586 1807 l 1596 1808 l 1605 1805 l 1613 1800 l 1620 1795 l 1629 1792 l 1639 1793 l 1650 1800 l 1657 1810 l 1659 1820 l 1659 1826 l 1656 1831 l 1654 1837 l 1651 1845 l 1650 1857 l 1650 1875 l 1650 1893 l 1651 1905 l 1654 1913 l 1656 1919 l 1659 1924 l 1659 1930 l 1657 1940 l 1650 1950 l 1639 1957 l 1629 1958 l 1620 1955 l 1613 1950 l 1605 1945 l 1596 1942 l 1586 1943 l 1575 1950 l 1568 1961 l 1567 1971 l 1570 1980 l 1575 1988 l 1580 1995 l 1583 2004 l 1582 2014 l 1575 2025 l 1564 2032 l 1554 2033 l 1545 2030 l 1538 2025 l 1530 2020 l 1521 2017 l 1511 2018 l 1500 2025 l 1493 2035 l 1491 2045 l 1491 2051 l 1494 2056 l 1496 2062 l 1499 2070 l 1500 2082 l 1500 2100 l 1500 2117 l 1500 2129 l 1500 2135 l 1500 2138 l 1500 2140 l 1500 2146 l 1500 2158 l 1500 2175 l 1500 2192 l 1500 2204 l 1500 2210 l 1500 2213 l 1500 2215 l 1500 2221 l 1500 2233 l 1500 2250 l 1500 2267 l 1500 2279 l 1500 2285 l 1500 2288 l 1500 2290 l 1500 2296 l 1500 2308 l 1500 2325 l 1500 2342 l 1500 2354 l 1500 2360 l 1500 2363 l 1500 2365 l 1500 2371 l 1500 2383 l 1500 2400 l 1500 2418 l 1499 2430 l 1496 2438 l 1494 2444 l 1491 2449 l 1491 2455 l 1493 2465 l 1500 2475 l 1511 2482 l 1521 2483 l 1530 2480 l 1538 2475 l 1545 2470 l 1554 2467 l 1564 2468 l 1575 2475 l 1582 2486 l 1583 2496 l 1580 2505 l 1575 2513 l 1570 2520 l 1567 2529 l 1568 2539 l 1575 2550 l 1586 2557 l 1596 2558 l 1605 2555 l 1613 2550 l 1620 2545 l 1629 2542 l 1639 2543 l 1650 2550 l 1655 2557 l 1659 2564 l 1661 2571 l 1662 2577 l 1662 2583 l 1662 2588 l 1662 2592 l 1662 2598 l 1661 2604 l 1659 2611 l 1655 2618 l 1650 2625 l 1639 2632 l 1629 2633 l 1620 2630 l 1613 2625 l 1605 2620 l 1596 2617 l 1586 2618 l 1575 2625 l 1568 2635 l 1566 2645 l 1566 2651 l 1569 2656 l 1571 2662 l 1574 2670 l 1575 2682 l 1575 2700 l 1575 2717 l 1575 2729 l 1575 2735 l 1575 2738 l 1575 2740 l 1575 2746 l 1575 2758 l 1575 2775 l 1575 2792 l 1575 2804 l 1575 2810 l 1575 2813 l 1575 2815 l 1575 2821 l 1575 2833 l 1575 2850 l 1575 2867 l 1575 2879 l 1575 2885 l 1575 2888 l 1575 2890 l 1575 2896 l 1575 2908 l 1575 2925 l 1575 2942 l 1575 2954 l 1575 2960 l 1575 2963 l 1575 2965 l 1575 2971 l 1575 2983 l 1575 3000 l 1575 3017 l 1575 3029 l 1575 3035 l 1575 3038 l 1575 3040 l 1575 3046 l 1575 3058 l 1575 3075 l 1575 3092 l 1575 3104 l 1575 3110 l 1575 3113 l 1575 3115 l 1575 3121 l 1575 3133 l 1575 3150 l 1575 3167 l 1575 3179 l 1575 3185 l 1575 3188 l 1575 3190 l 1575 3196 l 1575 3208 l 1575 3225 l 1575 3243 l 1576 3255 l 1579 3263 l 1581 3269 l 1584 3274 l 1584 3280 l 1582 3290 l 1575 3300 l 1564 3307 l 1554 3308 l 1545 3305 l 1538 3300 l 1530 3295 l 1521 3292 l 1511 3293 l 1500 3300 l 1493 3310 l 1491 3320 l 1491 3326 l 1494 3331 l 1496 3337 l 1499 3345 l 1500 3357 l 1500 3375 l 1500 3393 l 1499 3405 l 1496 3413 l 1494 3419 l 1491 3424 l 1491 3430 l 1493 3440 l 1500 3450 l 1511 3457 l 1521 3458 l 1530 3455 l 1538 3450 l 1545 3445 l 1554 3442 l 1564 3443 l 1575 3450 l 1582 3460 l 1584 3470 l 1584 3476 l 1581 3481 l 1579 3487 l 1576 3495 l 1575 3507 l 1575 3525 l 1575 3542 l 1575 3554 l 1575 3560 l 1575 3563 l 1575 3565 l 1575 3571 l 1575 3583 l 1575 3600 l 1575 3617 l 1575 3629 l 1575 3635 l 1575 3638 l 1575 3640 l 1575 3646 l 1575 3658 l 1575 3675 l 1575 3693 l 1576 3705 l 1579 3713 l 1581 3719 l 1584 3724 l 1584 3730 l 1582 3740 l 1575 3750 l 1564 3757 l 1554 3758 l 1545 3755 l 1538 3750 l 1530 3745 l 1521 3742 l 1511 3743 l 1500 3750 l 1493 3761 l 1492 3771 l 1495 3780 l 1500 3788 l 1505 3795 l 1508 3804 l 1507 3814 l 1500 3825 l 1489 3832 l 1479 3833 l 1470 3830 l 1463 3825 l 1455 3820 l 1446 3817 l 1436 3818 l 1425 3825 l 1418 3835 l 1416 3845 l 1416 3851 l 1419 3856 l 1421 3862 l 1424 3870 l 1425 3882 l 1425 3900 l 1425 3917 l 1425 3929 l 1425 3935 l 1425 3938 l 1425 3940 l 1425 3946 l 1425 3958 l 1425 3975 l 1425 3993 l 1426 4005 l 1429 4013 l 1431 4019 l 1434 4024 l 1434 4030 l 1432 4040 l 1425 4050 l 1414 4057 l 1404 4058 l 1395 4055 l 1388 4050 l 1380 4045 l 1371 4042 l 1361 4043 l 1350 4050 l 1343 4060 l 1341 4070 l 1341 4076 l 1344 4081 l 1346 4087 l 1349 4095 l 1350 4107 l 1350 4125 l 1350 4142 l 1350 4154 l 1350 4160 l 1350 4163 l 1350 4165 l 1350 4171 l 1350 4183 l 1350 4200 l 1350 4217 l 1349 4229 l 1346 4235 l 1344 4238 l 1341 4240 l 1341 4246 l 1343 4258 l 1350 4275 l 1358 4289 l 1367 4300 l 1375 4307 l 1382 4311 l 1388 4313 l 1393 4314 l 1400 4318 l 1408 4325 l 1417 4336 l 1425 4350 l 1432 4368 l 1433 4380 l 1430 4388 l 1425 4394 l 1420 4399 l 1417 4405 l 1418 4415 l 1425 4425 l 1435 4432 l 1445 4434 l 1451 4434 l 1456 4431 l 1462 4429 l 1470 4426 l 1482 4425 l 1500 4425 l 1518 4425 l 1532 4424 l 1542 4421 l 1550 4419 l 1557 4416 l 1564 4416 l 1571 4418 l 1575 4425 l 1572 4433 l 1567 4441 l 1559 4448 l 1552 4452 l 1544 4456 l 1536 4460 l 1527 4466 l 1518 4474 l 1509 4486 l 1500 4500 l 1493 4517 l 1491 4529 l 1491 4535 l 1494 4538 l 1496 4540 l 1499 4546 l 1500 4558 l 1500 4575 l 1500 4592 l 1500 4604 l 1500 4610 l 1500 4613 l 1500 4615 l 1500 4621 l 1500 4633 l 1500 4650 l 1500 4667 l 1500 4679 l 1500 4685 l 1500 4688 l 1500 4690 l 1500 4696 l 1500 4708 l 1500 4725 l 1500 4742 l 1500 4754 l 1500 4760 l 1500 4763 l 1500 4765 l 1500 4771 l 1500 4783 l 1500 4800 l 1500 4817 l 1500 4829 l 1500 4835 l 1500 4838 l 1500 4840 l 1500 4846 l 1500 4858 l 1500 4875 l 1500 4892 l 1500 4904 l 1500 4910 l 1500 4913 l 1500 4915 l 1500 4921 l 1500 4933 l 1500 4950 l 1500 4967 l 1500 4979 l 1500 4985 l 1500 4988 l 1500 4990 l 1500 4996 l 1500 5008 l 1500 5025 l 1500 5042 l 1500 5054 l 1500 5060 l 1500 5063 l 1500 5065 l 1500 5071 l 1500 5083 l 1500 5100 l 1500 5117 l 1500 5129 l 1500 5135 l 1500 5138 l 1500 5140 l 1500 5146 l 1500 5158 l 1500 5175 l 1500 5193 l 1499 5205 l 1496 5213 l 1494 5219 l 1491 5224 l 1491 5230 l 1493 5240 l 1500 5250 l 1511 5257 l 1521 5258 l 1530 5255 l 1538 5250 l 1545 5245 l 1554 5242 l 1564 5243 l 1575 5250 l 1582 5260 l 1584 5270 l 1584 5276 l 1581 5281 l 1579 5287 l 1576 5295 l 1575 5307 l 1575 5325 l 1575 5342 l 1575 5354 l 1575 5360 l 1575 5363 l 1575 5365 l 1575 5371 l 1575 5383 l 1575 5400 l 1575 5418 l 1576 5430 l 1579 5438 l 1581 5444 l 1584 5449 l 1584 5455 l 1582 5465 l 1575 5475 l 1565 5482 l 1555 5484 l 1549 5484 l 1544 5481 l 1538 5479 l 1530 5476 l 1518 5475 l 1500 5475 l 1482 5475 l 1470 5474 l 1462 5471 l 1456 5469 l 1451 5466 l 1445 5466 l 1435 5468 l 1425 5475 l 1418 5485 l 1416 5495 l 1416 5501 l 1419 5506 l 1421 5512 l 1424 5520 l 1425 5532 l 1425 5550 l 1425 5567 l 1425 5579 l 1425 5585 l 1425 5588 l 1425 5590 l 1425 5596 l 1425 5608 l 1425 5625 l 1425 5643 l 1426 5655 l 1429 5663 l 1431 5669 l 1434 5674 l 1434 5680 l 1432 5690 l 1425 5700 l 1414 5707 l 1404 5708 l 1395 5705 l 1388 5700 l 1380 5695 l 1371 5692 l 1361 5693 l 1350 5700 l 1343 5710 l 1341 5720 l 1341 5726 l 1344 5731 l 1346 5737 l 1349 5745 l 1350 5757 l 1350 5775 l 1350 5793 l 1349 5805 l 1346 5813 l 1344 5819 l 1341 5824 l 1341 5830 l 1343 5840 l 1350 5850 l 1361 5857 l 1371 5858 l 1380 5855 l 1388 5850 l 1395 5845 l 1404 5842 l 1414 5843 l 1425 5850 l 1432 5861 l 1433 5871 l 1430 5880 l 1425 5888 l 1420 5895 l 1417 5904 l 1418 5914 l 1425 5925 l 1436 5932 l 1446 5933 l 1455 5930 l 1463 5925 l 1470 5920 l 1479 5917 l 1489 5918 l 1500 5925 l 1507 5936 l 1508 5946 l 1505 5955 l 1500 5963 l 1495 5970 l 1492 5979 l 1493 5989 l 1500 6000 l 1510 6007 l 1520 6009 l 1526 6009 l 1531 6006 l 1537 6004 l 1545 6001 l 1557 6000 l 1575 6000 l 1593 6000 l 1605 5999 l 1613 5996 l 1619 5994 l 1624 5991 l 1630 5991 l 1640 5993 l 1650 6000 l 1657 6010 l 1659 6020 l 1659 6026 l 1656 6031 l 1654 6037 l 1651 6045 l 1650 6057 l 1650 6075 l 1650 6092 l 1650 6104 l 1650 6110 l 1650 6113 l 1650 6115 l 1650 6121 l 1650 6133 l 1650 6150 l 1650 6168 l 1651 6180 l 1654 6188 l 1656 6194 l 1659 6199 l 1659 6205 l 1657 6215 l 1650 6225 l 1640 6232 l 1630 6234 l 1624 6234 l 1619 6231 l 1613 6229 l 1605 6226 l 1593 6225 l 1575 6225 l 1558 6225 l 1546 6225 l 1540 6225 l 1538 6225 l 1535 6225 l 1529 6225 l 1517 6225 l 1500 6225 l 1482 6225 l 1470 6226 l 1462 6229 l 1456 6231 l 1451 6234 l 1445 6234 l 1435 6232 l 1425 6225 l 1418 6214 l 1417 6204 l 1420 6195 l 1425 6188 l 1430 6180 l 1433 6171 l 1432 6161 l 1425 6150 l 1417 6144 l 1408 6140 l 1400 6139 l 1393 6138 l 1387 6138 l 1382 6138 l 1375 6139 l 1367 6140 l 1358 6144 l 1350 6150 l 1343 6161 l 1342 6171 l 1345 6180 l 1350 6188 l 1355 6195 l 1358 6204 l 1357 6214 l 1350 6225 l 1339 6232 l 1329 6233 l 1320 6230 l 1313 6225 l 1305 6220 l 1296 6217 l 1286 6218 l 1275 6225 l 1268 6235 l 1266 6245 l 1266 6251 l 1269 6256 l 1271 6262 l 1274 6270 l 1275 6282 l 1275 6300 l 1275 6318 l 1274 6330 l 1271 6338 l 1269 6344 l 1266 6349 l 1266 6355 l 1268 6365 l 1275 6375 l 1286 6382 l 1296 6383 l 1305 6380 l 1313 6375 l 1320 6370 l 1329 6367 l 1339 6368 l 1350 6375 l 1357 6385 l 1359 6395 l 1359 6401 l 1356 6406 l 1354 6412 l 1351 6420 l 1350 6432 l 1350 6450 l 1350 6468 l 1349 6480 l 1346 6488 l 1344 6494 l 1341 6499 l 1341 6505 l 1343 6515 l 1350 6525 l 1361 6532 l 1371 6533 l 1380 6530 l 1388 6525 l 1395 6520 l 1404 6517 l 1414 6518 l 1425 6525 l 1432 6536 l 1433 6546 l 1430 6555 l 1425 6563 l 1420 6570 l 1417 6579 l 1418 6589 l 1425 6600 l 1436 6607 l 1446 6608 l 1455 6605 l 1463 6600 l 1470 6595 l 1479 6592 l 1489 6593 l 1500 6600 l 1507 6611 l 1508 6621 l 1505 6630 l 1500 6638 l 1495 6645 l 1492 6654 l 1493 6664 l 1500 6675 l 1510 6682 l 1520 6684 l 1526 6684 l 1531 6681 l 1537 6679 l 1545 6676 l 1557 6675 l 1575 6675 l 1593 6675 l 1605 6674 l 1613 6671 l 1619 6669 l 1624 6666 l 1630 6666 l 1640 6668 l 1650 6675 l 1657 6686 l 1658 6696 l 1655 6705 l 1650 6713 l 1645 6720 l 1642 6729 l 1643 6739 l 1650 6750 l 1660 6757 l 1670 6759 l 1676 6759 l 1681 6756 l 1687 6754 l 1695 6751 l 1707 6750 l 1725 6750 l 1743 6750 l 1755 6749 l 1763 6746 l 1769 6744 l 1774 6741 l 1780 6741 l 1790 6743 l 1800 6750 l 1805 6757 l 1809 6764 l 1811 6771 l 1812 6777 l 1812 6783 l 1812 6788 l 1812 6792 l 1812 6798 l 1811 6804 l 1809 6811 l 1805 6818 l 1800 6825 l 1789 6832 l 1779 6833 l 1770 6830 l 1763 6825 l 1755 6820 l 1746 6817 l 1736 6818 l 1725 6825 l 1718 6835 l 1716 6845 l 1716 6851 l 1719 6856 l 1721 6862 l 1724 6870 l 1725 6882 l 1725 6900 l 1725 6918 l 1724 6930 l 1721 6938 l 1719 6944 l 1716 6949 l 1716 6955 l 1718 6965 l 1725 6975 l 1736 6982 l 1746 6983 l 1755 6980 l 1763 6975 l 1770 6970 l 1779 6967 l 1789 6968 l 1800 6975 l 1807 6986 l 1808 6996 l 1805 7005 l 1800 7013 l 1795 7020 l 1792 7029 l 1793 7039 l 1800 7050 l 1810 7057 l 1820 7059 l 1826 7059 l 1831 7056 l 1837 7054 l 1845 7051 l 1857 7050 l 1875 7050 l 1892 7050 l 1904 7049 l 1910 7046 l 1913 7044 l 1915 7041 l 1921 7041 l 1933 7043 l 1950 7050 l 1964 7058 l 1975 7067 l 1982 7075 l 1986 7082 l 1988 7088 l 1989 7093 l 1993 7100 l 2000 7108 l 2011 7117 l 2025 7125 l 2042 7132 l 2054 7134 l 2060 7134 l 2063 7131 l 2065 7129 l 2071 7126 l 2083 7125 l 2100 7125 l 2118 7125 l 2130 7126 l 2138 7129 l 2144 7131 l 2149 7134 l 2155 7134 l 2165 7132 l 2175 7125 l 2182 7114 l 2183 7104 l 2180 7095 l 2175 7088 l 2170 7080 l 2167 7071 l 2168 7061 l 2175 7050 l 2186 7043 l 2196 7042 l 2205 7045 l 2213 7050 l 2220 7055 l 2229 7058 l 2239 7057 l 2250 7050 l 2257 7039 l 2258 7029 l 2255 7020 l 2250 7013 l 2245 7005 l 2242 6996 l 2243 6986 l 2250 6975 l 2260 6968 l 2270 6966 l 2276 6966 l 2281 6969 l 2287 6971 l 2295 6974 l 2307 6975 l 2325 6975 l 2342 6975 l 2354 6975 l 2360 6975 l 2363 6975 l 2365 6975 l 2371 6975 l 2383 6975 l 2400 6975 l 2418 6975 l 2430 6976 l 2438 6979 l 2444 6981 l 2449 6984 l 2455 6984 l 2465 6982 l 2475 6975 l 2482 6964 l 2483 6954 l 2480 6945 l 2475 6938 l 2470 6930 l 2467 6921 l 2468 6911 l 2475 6900 l 2485 6893 l 2495 6891 l 2501 6891 l 2506 6894 l 2512 6896 l 2520 6899 l 2532 6900 l 2550 6900 l 2568 6900 l 2580 6901 l 2588 6904 l 2594 6906 l 2599 6909 l 2605 6909 l 2615 6907 l 2625 6900 l 2632 6889 l 2633 6879 l 2630 6870 l 2625 6863 l 2620 6855 l 2617 6846 l 2618 6836 l 2625 6825 l 2633 6819 l 2642 6815 l 2650 6814 l 2657 6813 l 2663 6813 l 2668 6813 l 2675 6814 l 2683 6815 l 2692 6819 l 2700 6825 l 2707 6836 l 2708 6846 l 2705 6855 l 2700 6863 l 2695 6870 l 2692 6879 l 2693 6889 l 2700 6900 l 2710 6907 l 2720 6909 l 2726 6909 l 2731 6906 l 2737 6904 l 2745 6901 l 2757 6900 l 2775 6900 l 2792 6900 l 2804 6899 l 2810 6896 l 2813 6894 l 2815 6891 l 2821 6891 l 2833 6893 l 2850 6900 l 2864 6908 l 2875 6917 l 2882 6925 l 2886 6932 l 2888 6938 l 2889 6943 l 2893 6950 l 2900 6958 l 2911 6967 l 2925 6975 l 2942 6982 l 2954 6984 l 2960 6984 l 2963 6981 l 2965 6979 l 2971 6976 l 2983 6975 l 3000 6975 l 3017 6975 l 3029 6975 l 3035 6975 l 3038 6975 l 3040 6975 l 3046 6975 l 3058 6975 l 3075 6975 l 3092 6975 l 3104 6975 l 3110 6975 l 3113 6975 l 3115 6975 l 3121 6975 l 3133 6975 l 3150 6975 l 3167 6975 l 3179 6975 l 3185 6975 l 3188 6975 l 3190 6975 l 3196 6975 l 3208 6975 l 3225 6975 l 3242 6975 l 3254 6975 l 3260 6975 l 3263 6975 l 3265 6975 l 3271 6975 l 3283 6975 l 3300 6975 l 3317 6975 l 3329 6975 l 3335 6975 l 3338 6975 l 3340 6975 l 3346 6975 l 3358 6975 l 3375 6975 l 3392 6975 l 3404 6975 l 3410 6975 l 3413 6975 l 3415 6975 l 3421 6975 l 3433 6975 l 3450 6975 l 3467 6975 l 3479 6975 l 3485 6975 l 3488 6975 l 3490 6975 l 3496 6975 l 3508 6975 l 3525 6975 l 3542 6975 l 3554 6975 l 3560 6975 l 3563 6975 l 3565 6975 l 3571 6975 l 3583 6975 l 3600 6975 l 3617 6975 l 3629 6975 l 3635 6975 l 3638 6975 l 3640 6975 l 3646 6975 l 3658 6975 l 3675 6975 l 3692 6975 l 3704 6975 l 3710 6975 l 3713 6975 l 3715 6975 l 3721 6975 l 3733 6975 l 3750 6975 l 3767 6975 l 3779 6975 l 3785 6975 l 3788 6975 l 3790 6975 l 3796 6975 l 3808 6975 l 3825 6975 l 3843 6975 l 3855 6974 l 3863 6971 l 3869 6969 l 3874 6966 l 3880 6966 l 3890 6968 l 3900 6975 l 3907 6986 l 3908 6996 l 3905 7005 l 3900 7013 l 3895 7020 l 3892 7029 l 3893 7039 l 3900 7050 l 3910 7057 l 3920 7059 l 3926 7059 l 3931 7056 l 3937 7054 l 3945 7051 l 3957 7050 l 3975 7050 l 3992 7050 l 4004 7050 l 4010 7050 l 4013 7050 l 4015 7050 l 4021 7050 l 4033 7050 l 4050 7050 l 4068 7050 l 4080 7051 l 4088 7054 l 4094 7056 l 4099 7059 l 4105 7059 l 4115 7057 l 4125 7050 l 4132 7040 l 4133 7030 l 4130 7024 l 4125 7019 l 4120 7013 l 4117 7005 l 4118 6993 l 4125 6975 l 4133 6961 l 4141 6949 l 4148 6941 l 4152 6935 l 4156 6931 l 4160 6927 l 4166 6923 l 4174 6916 l 4186 6908 l 4200 6900 l 4217 6893 l 4229 6891 l 4235 6891 l 4238 6894 l 4240 6896 l 4246 6899 l 4258 6900 l 4275 6900 l 4293 6900 l 4305 6899 l 4313 6896 l 4319 6894 l 4324 6891 l 4330 6891 l 4340 6893 l 4350 6900 l 4357 6911 l 4358 6921 l 4355 6930 l 4350 6938 l 4345 6945 l 4342 6954 l 4343 6964 l 4350 6975 l 4360 6982 l 4370 6984 l 4376 6984 l 4381 6981 l 4387 6979 l 4395 6976 l 4407 6975 l 4425 6975 l 4442 6975 l 4454 6975 l 4460 6975 l 4463 6975 l 4465 6975 l 4471 6975 l 4483 6975 l 4500 6975 l 4518 6975 l 4530 6976 l 4538 6979 l 4544 6981 l 4549 6984 l 4555 6984 l 4565 6982 l 4575 6975 l 4582 6964 l 4583 6954 l 4580 6945 l 4575 6938 l 4570 6930 l 4567 6921 l 4568 6911 l 4575 6900 l 4585 6893 l 4595 6891 l 4601 6891 l 4606 6894 l 4612 6896 l 4620 6899 l 4632 6900 l 4650 6900 l 4667 6900 l 4679 6900 l 4685 6900 l 4688 6900 l 4690 6900 l 4696 6900 l 4708 6900 l 4725 6900 l 4742 6900 l 4754 6899 l 4760 6896 l 4763 6894 l 4765 6891 l 4771 6891 l 4783 6893 l 4800 6900 l 4814 6908 l 4824 6917 l 4830 6925 l 4831 6932 l 4831 6938 l 4831 6943 l 4834 6950 l 4841 6958 l 4855 6967 l 4875 6975 l 4894 6980 l 4911 6983 l 4925 6984 l 4936 6984 l 4944 6983 l 4950 6981 l 4956 6979 l 4964 6978 l 4975 6976 l 4989 6976 l 5006 6975 l 5025 6975 l 5049 6975 l 5062 6975 l 5065 6975 l 5063 6975 l 5060 6975 l 5063 6975 l 5076 6975 l 5100 6975 l 5119 6975 l 5136 6975 l 5150 6975 l 5161 6975 l 5169 6975 l 5175 6975 l 5181 6975 l 5189 6975 l 5200 6975 l 5214 6975 l 5231 6975 l 5250 6975 l 5274 6975 l 5288 6975 l 5293 6975 l 5294 6975 l 5297 6975 l 5308 6975 l 5325 6975 l 5342 6975 l 5354 6974 l 5360 6971 l 5363 6969 l 5365 6966 l 5371 6966 l 5383 6968 l 5400 6975 l 5414 6983 l 5425 6992 l 5432 7000 l 5436 7007 l 5438 7013 l 5439 7018 l 5443 7025 l 5450 7033 l 5461 7042 l 5475 7050 l 5487 7055 l 5497 7059 l 5505 7061 l 5511 7062 l 5515 7062 l 5519 7062 l 5522 7062 l 5526 7062 l 5530 7061 l 5536 7059 l 5543 7055 l 5550 7050 l 5557 7039 l 5558 7029 l 5555 7020 l 5550 7013 l 5545 7005 l 5542 6996 l 5543 6986 l 5550 6975 l 5560 6968 l 5570 6966 l 5576 6966 l 5581 6969 l 5587 6971 l 5595 6974 l 5607 6975 l 5625 6975 l 5642 6975 l 5654 6975 l 5660 6975 l 5663 6975 l 5665 6975 l 5671 6975 l 5683 6975 l 5700 6975 l 5717 6975 l 5729 6975 l 5735 6975 l 5738 6975 l 5740 6975 l 5746 6975 l 5758 6975 l 5775 6975 l 5792 6975 l 5804 6975 l 5810 6975 l 5813 6975 l 5815 6975 l 5821 6975 l 5833 6975 l 5850 6975 l 5867 6975 l 5879 6975 l 5885 6975 l 5888 6975 l 5890 6975 l 5896 6975 l 5908 6975 l 5925 6975 l 5942 6975 l 5954 6975 l 5960 6975 l 5963 6975 l 5965 6975 l 5971 6975 l 5983 6975 l 6000 6975 l 6017 6975 l 6029 6975 l 6035 6975 l 6038 6975 l 6040 6975 l 6046 6975 l 6058 6975 l 6075 6975 l 6092 6975 l 6104 6975 l 6110 6975 l 6113 6975 l 6115 6975 l 6121 6975 l 6133 6975 l 6150 6975 l 6167 6975 l 6179 6975 l 6185 6975 l 6188 6975 l 6190 6975 l 6196 6975 l 6208 6975 l 6225 6975 l 6242 6975 l 6254 6975 l 6260 6975 l 6263 6975 l 6265 6975 l 6271 6975 l 6283 6975 l 6300 6975 l 6317 6975 l 6329 6975 l 6335 6975 l 6338 6975 l 6340 6975 l 6346 6975 l 6358 6975 l 6375 6975 l 6392 6975 l 6404 6975 l 6410 6975 l 6413 6975 l 6415 6975 l 6421 6975 l 6433 6975 l 6450 6975 l 6467 6975 l 6479 6975 l 6485 6975 l 6488 6975 l 6490 6975 l 6496 6975 l 6508 6975 l 6525 6975 l 6542 6975 l 6554 6975 l 6560 6975 l 6563 6975 l 6565 6975 l 6571 6975 l 6583 6975 l 6600 6975 l 6617 6975 l 6629 6975 l 6635 6975 l 6638 6975 l 6640 6975 l 6646 6975 l 6658 6975 l 6675 6975 l 6692 6975 l 6704 6975 l 6710 6975 l 6713 6975 l 6715 6975 l 6721 6975 l 6733 6975 l 6750 6975 l 6768 6975 l 6780 6976 l 6788 6979 l 6794 6981 l 6799 6984 l 6805 6984 l 6815 6982 l 6825 6975 l 6832 6964 l 6833 6954 l 6830 6945 l 6825 6938 l 6820 6930 l 6817 6921 l 6818 6911 l 6825 6900 l 6835 6893 l 6845 6891 l 6851 6891 l 6856 6894 l 6862 6896 l 6870 6899 l 6882 6900 l 6900 6900 l 6917 6900 l 6929 6900 l 6935 6900 l 6938 6900 l 6940 6900 l 6946 6900 l 6958 6900 l 6975 6900 l 6993 6900 l 7005 6901 l 7013 6904 l 7019 6906 l 7024 6909 l 7030 6909 l 7040 6907 l 7050 6900 l 7055 6893 l 7059 6886 l 7061 6879 l 7062 6873 l 7062 6867 l 7062 6862 l 7062 6858 l 7062 6852 l 7061 6846 l 7059 6839 l 7055 6832 l 7050 6825 l 7039 6818 l 7029 6817 l 7020 6820 l 7013 6825 l 7005 6830 l 6996 6833 l 6986 6832 l 6975 6825 l 6968 6815 l 6966 6805 l 6966 6799 l 6969 6794 l 6971 6788 l 6974 6780 l 6975 6768 l 6975 6750 l 6975 6733 l 6976 6721 l 6979 6715 l 6981 6713 l 6984 6710 l 6984 6704 l 6982 6692 l 6975 6675 l 6967 6661 l 6958 6650 l 6950 6643 l 6943 6639 l 6937 6637 l 6932 6636 l 6925 6632 l 6917 6625 l 6908 6614 l 6900 6600 l 6894 6586 l 6890 6574 l 6889 6566 l 6888 6560 l 6888 6556 l 6888 6552 l 6889 6548 l 6890 6541 l 6894 6533 l 6900 6525 l 6911 6518 l 6921 6517 l 6930 6520 l 6938 6525 l 6945 6530 l 6954 6533 l 6964 6532 l 6975 6525 l 6982 6515 l 6984 6505 l 6984 6499 l 6981 6494 l 6979 6488 l 6976 6480 l 6975 6468 l 6975 6450 l 6975 6433 l 6976 6421 l 6979 6415 l 6981 6413 l 6984 6410 l 6984 6404 l 6982 6392 l 6975 6375 l 6967 6361 l 6958 6350 l 6950 6343 l 6943 6339 l 6937 6337 l 6932 6336 l 6925 6332 l 6917 6325 l 6908 6314 l 6900 6300 l 6893 6283 l 6891 6271 l 6891 6265 l 6894 6263 l 6896 6260 l 6899 6254 l 6900 6242 l 6900 6225 l 6900 6208 l 6901 6196 l 6904 6190 l 6906 6188 l 6909 6185 l 6909 6179 l 6907 6167 l 6900 6150 l 6892 6136 l 6883 6125 l 6875 6118 l 6868 6114 l 6862 6112 l 6857 6111 l 6850 6107 l 6842 6100 l 6833 6089 l 6825 6075 l 6818 6058 l 6816 6046 l 6816 6040 l 6819 6038 l 6821 6035 l 6824 6029 l 6825 6017 l 6825 6000 l 6825 5983 l 6825 5971 l 6825 5965 l 6825 5963 l 6825 5960 l 6825 5954 l 6825 5942 l 6825 5925 l 6825 5908 l 6825 5896 l 6825 5890 l 6825 5888 l 6825 5885 l 6825 5879 l 6825 5867 l 6825 5850 l 6825 5832 l 6824 5820 l 6821 5812 l 6819 5806 l 6816 5801 l 6816 5795 l 6818 5785 l 6825 5775 l 6835 5768 l 6845 5767 l 6851 5770 l 6856 5775 l 6862 5780 l 6870 5783 l 6882 5782 l 6900 5775 l 6914 5767 l 6926 5759 l 6934 5752 l 6940 5748 l 6944 5744 l 6948 5740 l 6952 5734 l 6959 5726 l 6967 5714 l 6975 5700 l 6982 5682 l 6983 5670 l 6980 5662 l 6975 5656 l 6970 5651 l 6967 5645 l 6968 5635 l 6975 5625 l 6986 5618 l 6996 5617 l 7005 5620 l 7013 5625 l 7020 5630 l 7029 5633 l 7039 5632 l 7050 5625 l 7057 5615 l 7059 5605 l 7059 5599 l 7056 5594 l 7054 5588 l 7051 5580 l 7050 5568 l 7050 5550 l 7050 5532 l 7051 5520 l 7054 5512 l 7056 5506 l 7059 5501 l 7059 5495 l 7057 5485 l 7050 5475 l 7039 5468 l 7029 5467 l 7020 5470 l 7013 5475 l 7005 5480 l 6996 5483 l 6986 5482 l 6975 5475 l 6968 5465 l 6966 5455 l 6966 5449 l 6969 5444 l 6971 5438 l 6974 5430 l 6975 5418 l 6975 5400 l 6975 5383 l 6975 5371 l 6975 5365 l 6975 5363 l 6975 5360 l 6975 5354 l 6975 5342 l 6975 5325 l 6975 5308 l 6975 5296 l 6975 5290 l 6975 5288 l 6975 5285 l 6975 5279 l 6975 5267 l 6975 5250 l 6975 5233 l 6975 5221 l 6975 5215 l 6975 5213 l 6975 5210 l 6975 5204 l 6975 5192 l 6975 5175 l 6975 5158 l 6975 5146 l 6975 5140 l 6975 5138 l 6975 5135 l 6975 5129 l 6975 5117 l 6975 5100 l 6975 5083 l 6975 5072 l 6975 5069 l 6975 5068 l 6975 5063 l 6975 5049 l 6975 5025 l 6975 5006 l 6975 4989 l 6975 4975 l 6975 4964 l 6975 4956 l 6975 4950 l 6975 4944 l 6975 4936 l 6975 4925 l 6975 4911 l 6975 4894 l 6975 4875 l 6975 4851 l 6975 4838 l 6975 4835 l 6975 4838 l 6975 4840 l 6975 4837 l 6975 4824 l 6975 4800 l 6975 4781 l 6975 4764 l 6975 4751 l 6975 4742 l 6975 4736 l 6975 4731 l 6975 4726 l 6975 4720 l 6975 4709 l 6975 4694 l 6975 4674 l 6975 4650 l 6975 4626 l 6975 4606 l 6975 4591 l 6975 4580 l 6975 4574 l 6975 4569 l 6975 4564 l 6975 4558 l 6975 4549 l 6975 4536 l 6975 4519 l 6975 4500 l 6975 4476 l 6975 4462 l 6975 4457 l 6975 4456 l 6975 4453 l 6975 4442 l 6975 4425 l 6975 4408 l 6975 4396 l 6975 4390 l 6975 4388 l 6975 4385 l 6975 4379 l 6975 4367 l 6975 4350 l 6975 4333 l 6975 4321 l 6975 4315 l 6975 4313 l 6975 4310 l 6975 4304 l 6975 4292 l 6975 4275 l 6975 4258 l 6975 4246 l 6975 4240 l 6975 4238 l 6975 4235 l 6975 4229 l 6975 4217 l 6975 4200 l 6975 4183 l 6975 4171 l 6975 4165 l 6975 4163 l 6975 4160 l 6975 4154 l 6975 4142 l 6975 4125 l 6975 4107 l 6976 4095 l 6979 4087 l 6981 4081 l 6984 4076 l 6984 4070 l 6982 4060 l 6975 4050 l 6964 4043 l 6954 4042 l 6945 4045 l 6938 4050 l 6930 4055 l 6921 4058 l 6911 4057 l 6900 4050 l 6893 4040 l 6891 4030 l 6891 4024 l 6894 4019 l 6896 4013 l 6899 4005 l 6900 3993 l 6900 3975 l 6900 3957 l 6901 3945 l 6904 3937 l 6906 3931 l 6909 3926 l 6909 3920 l 6907 3910 l 6900 3900 l 6889 3893 l 6879 3892 l 6870 3895 l 6863 3900 l 6855 3905 l 6846 3908 l 6836 3907 l 6825 3900 l 6818 3890 l 6816 3880 l 6816 3874 l 6819 3869 l 6821 3863 l 6824 3855 l 6825 3843 l 6825 3825 l 6825 3808 l 6825 3796 l 6825 3790 l 6825 3788 l 6825 3785 l 6825 3779 l 6825 3767 l 6825 3750 l 6825 3733 l 6825 3721 l 6825 3715 l 6825 3713 l 6825 3710 l 6825 3704 l 6825 3692 l 6825 3675 l 6825 3658 l 6825 3646 l 6825 3640 l 6825 3638 l 6825 3635 l 6825 3629 l 6825 3617 l 6825 3600 l 6825 3583 l 6825 3571 l 6825 3565 l 6825 3563 l 6825 3560 l 6825 3554 l 6825 3542 l 6825 3525 l 6825 3508 l 6825 3496 l 6825 3490 l 6825 3488 l 6825 3485 l 6825 3479 l 6825 3467 l 6825 3450 l 6825 3432 l 6824 3420 l 6821 3412 l 6819 3406 l 6816 3401 l 6816 3395 l 6818 3385 l 6825 3375 l 6836 3368 l 6846 3367 l 6855 3370 l 6863 3375 l 6870 3380 l 6879 3383 l 6889 3382 l 6900 3375 l 6907 3365 l 6909 3355 l 6909 3349 l 6906 3344 l 6904 3338 l 6901 3330 l 6900 3318 l 6900 3300 l 6900 3283 l 6900 3271 l 6900 3265 l 6900 3263 l 6900 3260 l 6900 3254 l 6900 3242 l 6900 3225 l 6900 3208 l 6900 3196 l 6900 3190 l 6900 3188 l 6900 3185 l 6900 3179 l 6900 3167 l 6900 3150 l 6900 3133 l 6899 3121 l 6896 3115 l 6894 3113 l 6891 3110 l 6891 3104 l 6893 3092 l 6900 3075 l 6908 3061 l 6917 3050 l 6925 3043 l 6932 3039 l 6938 3037 l 6943 3036 l 6950 3032 l 6958 3025 l 6967 3014 l 6975 3000 l 6982 2983 l 6984 2971 l 6984 2965 l 6981 2963 l 6979 2960 l 6976 2954 l 6975 2942 l 6975 2925 l 6975 2908 l 6975 2896 l 6975 2890 l 6975 2888 l 6975 2885 l 6975 2879 l 6975 2867 l 6975 2850 l 6975 2833 l 6975 2821 l 6975 2815 l 6975 2813 l 6975 2810 l 6975 2804 l 6975 2792 l 6975 2775 l 6975 2758 l 6975 2746 l 6975 2740 l 6975 2738 l 6975 2735 l 6975 2729 l 6975 2717 l 6975 2700 l 6975 2682 l 6974 2670 l 6971 2662 l 6969 2656 l 6966 2651 l 6966 2645 l 6968 2635 l 6975 2625 l 6986 2618 l 6996 2617 l 7005 2620 l 7013 2625 l 7020 2630 l 7029 2633 l 7039 2632 l 7050 2625 l 7055 2618 l 7059 2611 l 7061 2605 l 7062 2601 l 7062 2597 l 7062 2594 l 7062 2590 l 7062 2586 l 7061 2580 l 7059 2572 l 7055 2562 l 7050 2550 l 7042 2536 l 7033 2525 l 7025 2518 l 7018 2514 l 7012 2512 l 7007 2511 l 7000 2507 l 6992 2500 l 6983 2489 l 6975 2475 l 6968 2458 l 6966 2446 l 6966 2440 l 6969 2438 l 6971 2435 l 6974 2429 l 6975 2417 l 6975 2400 l 6975 2383 l 6975 2371 l 6975 2365 l 6975 2363 l 6975 2360 l 6975 2354 l 6975 2342 l 6975 2325 l 6975 2308 l 6975 2296 l 6975 2290 l 6975 2288 l 6975 2285 l 6975 2279 l 6975 2267 l 6975 2250 l 6975 2233 l 6975 2221 l 6975 2215 l 6975 2213 l 6975 2210 l 6975 2204 l 6975 2192 l 6975 2175 l 6975 2158 l 6975 2146 l 6975 2140 l 6975 2138 l 6975 2135 l 6975 2129 l 6975 2117 l 6975 2100 l 6975 2083 l 6975 2071 l 6975 2065 l 6975 2063 l 6975 2060 l 6975 2054 l 6975 2042 l 6975 2025 l 6975 2008 l 6975 1996 l 6975 1990 l 6975 1988 l 6975 1985 l 6975 1979 l 6975 1967 l 6975 1950 l 6975 1933 l 6975 1921 l 6975 1915 l 6975 1913 l 6975 1910 l 6975 1904 l 6975 1892 l 6975 1875 l 6975 1858 l 6975 1846 l 6975 1840 l 6975 1838 l 6975 1835 l 6975 1829 l 6975 1817 l 6975 1800 l 6975 1782 l 6976 1770 l 6979 1762 l 6981 1756 l 6984 1751 l 6984 1745 l 6982 1735 l 6975 1725 l 6964 1718 l 6954 1717 l 6945 1720 l 6938 1725 l 6930 1730 l 6921 1733 l 6911 1732 l 6900 1725 l 6893 1714 l 6892 1704 l 6895 1695 l 6900 1688 l 6905 1680 l 6908 1671 l 6907 1661 l 6900 1650 l 6889 1643 l 6879 1642 l 6870 1645 l 6863 1650 l 6855 1655 l 6846 1658 l 6836 1657 l 6825 1650 l 6818 1639 l 6817 1629 l 6820 1620 l 6825 1613 l 6830 1605 l 6833 1596 l 6832 1586 l 6825 1575 l 6815 1568 l 6805 1566 l 6799 1566 l 6794 1569 l 6788 1571 l 6780 1574 l 6768 1575 l 6750 1575 l 6733 1575 l 6721 1575 l 6715 1575 l 6713 1575 l 6710 1575 l 6704 1575 l 6692 1575 l 6675 1575 l 6658 1575 l 6646 1575 l 6640 1575 l 6638 1575 l 6635 1575 l 6629 1575 l 6617 1575 l 6600 1575 l 6583 1575 l 6571 1575 l 6565 1575 l 6563 1575 l 6560 1575 l 6554 1575 l 6542 1575 l 6525 1575 l 6508 1575 l 6496 1575 l 6490 1575 l 6488 1575 l 6485 1575 l 6479 1575 l 6467 1575 l 6450 1575 l 6432 1575 l 6420 1576 l 6412 1579 l 6406 1581 l 6401 1584 l 6395 1584 l 6385 1582 l 6375 1575 l 6368 1564 l 6367 1554 l 6370 1545 l 6375 1538 l 6380 1530 l 6383 1521 l 6382 1511 l 6375 1500 l 6365 1493 l 6355 1491 l 6349 1491 l 6344 1494 l 6338 1496 l 6330 1499 l 6318 1500 l 6300 1500 l 6283 1500 l 6271 1500 l 6265 1500 l 6263 1500 l 6260 1500 l 6254 1500 l 6242 1500 l 6225 1500 l 6208 1500 l 6196 1500 l 6190 1500 l 6188 1500 l 6185 1500 l 6179 1500 l 6167 1500 l 6150 1500 l 6133 1500 l 6121 1500 l 6115 1500 l 6113 1500 l 6110 1500 l 6104 1500 l 6092 1500 l 6075 1500 l 6058 1500 l 6046 1500 l 6040 1500 l 6038 1500 l 6035 1500 l 6029 1500 l 6017 1500 l 6000 1500 l 5983 1500 l 5971 1500 l 5965 1500 l 5963 1500 l 5960 1500 l 5954 1500 l 5942 1500 l 5925 1500 l 5908 1500 l 5896 1500 l 5890 1500 l 5888 1500 l 5885 1500 l 5879 1500 l 5867 1500 l 5850 1500 l 5832 1500 l 5820 1501 l 5812 1504 l 5806 1506 l 5801 1509 l 5795 1509 l 5785 1507 l 5775 1500 l 5768 1489 l 5767 1479 l 5770 1470 l 5775 1463 l 5780 1455 l 5783 1446 l 5782 1436 l 5775 1425 l 5765 1418 l 5755 1416 l 5749 1416 l 5744 1419 l 5738 1421 l 5730 1424 l 5718 1425 l 5700 1425 l 5683 1425 l 5671 1425 l 5665 1425 l 5663 1425 l 5660 1425 l 5654 1425 l 5642 1425 l 5625 1425 l 5608 1425 l 5596 1425 l 5590 1425 l 5588 1425 l 5585 1425 l 5579 1425 l 5567 1425 l 5550 1425 l 5533 1425 l 5521 1425 l 5515 1425 l 5513 1425 l 5510 1425 l 5504 1425 l 5492 1425 l 5475 1425 l 5458 1425 l 5446 1425 l 5440 1425 l 5438 1425 l 5435 1425 l 5429 1425 l 5417 1425 l 5400 1425 l 5383 1425 l 5371 1425 l 5365 1425 l 5363 1425 l 5360 1425 l 5354 1425 l 5342 1425 l 5325 1425 l 5308 1425 l 5296 1425 l 5290 1425 l 5288 1425 l 5285 1425 l 5279 1425 l 5267 1425 l 5250 1425 l 5233 1425 l 5221 1425 l 5215 1425 l 5213 1425 l 5210 1425 l 5204 1425 l 5192 1425 l 5175 1425 l 5158 1425 l 5146 1425 l 5140 1425 l 5138 1425 l 5135 1425 l 5129 1425 l 5117 1425 l 5100 1425 l 5083 1425 l 5071 1424 l 5065 1421 l 5063 1419 l 5060 1416 l 5054 1416 l 5042 1418 l 5025 1425 l 5011 1433 l 5000 1442 l 4993 1450 l 4989 1457 l 4987 1463 l 4986 1468 l 4982 1475 l 4975 1483 l 4964 1492 l 4950 1500 l 4933 1507 l 4921 1509 l 4915 1509 l 4913 1506 l 4910 1504 l 4904 1501 l 4892 1500 l 4875 1500 l 4858 1500 l 4846 1500 l 4840 1500 l 4838 1500 l 4835 1500 l 4829 1500 l 4817 1500 l 4800 1500 l 4783 1500 l 4771 1500 l 4765 1500 l 4763 1500 l 4760 1500 l 4754 1500 l 4742 1500 l 4725 1500 l 4707 1500 l 4695 1499 l 4687 1496 l 4681 1494 l 4676 1491 l 4670 1491 l 4660 1493 l 4650 1500 l 4643 1511 l 4642 1521 l 4645 1530 l 4650 1538 l 4655 1545 l 4658 1554 l 4657 1564 l 4650 1575 l 4643 1580 l 4636 1584 l 4629 1586 l 4623 1587 l 4617 1587 l 4612 1587 l 4608 1587 l 4602 1587 l 4596 1586 l 4589 1584 l 4582 1580 l 4575 1575 l 4568 1564 l 4567 1554 l 4570 1545 l 4575 1538 l 4580 1530 l 4583 1521 l 4582 1511 l 4575 1500 l 4565 1493 l 4555 1491 l 4549 1491 l 4544 1494 l 4538 1496 l 4530 1499 l 4518 1500 l 4500 1500 l 4483 1500 l 4471 1500 l 4465 1500 l 4463 1500 l 4460 1500 l 4454 1500 l 4442 1500 l 4425 1500 l 4408 1500 l 4396 1500 l 4390 1500 l 4388 1500 l 4385 1500 l 4379 1500 l 4367 1500 l 4350 1500 l 4333 1500 l 4322 1500 l 4319 1500 l 4318 1500 l 4313 1500 l 4299 1500 l 4275 1500 l 4256 1500 l 4239 1500 l 4225 1500 l 4214 1500 l 4206 1500 l 4200 1500 l 4194 1500 l 4186 1500 l 4175 1500 l 4161 1500 l 4144 1500 l 4125 1500 l 4101 1500 l 4087 1500 l 4082 1500 l 4081 1500 l 4078 1500 l 4067 1500 l 4050 1500 l 4033 1500 l 4021 1501 l 4015 1504 l 4013 1506 l 4010 1509 l 4004 1509 l 3992 1507 l 3975 1500 l 3961 1492 l 3951 1483 l 3945 1475 l 3944 1468 l 3944 1462 l 3944 1457 l 3941 1450 l 3934 1442 l 3920 1433 l 3900 1425 l 3881 1420 l 3864 1417 l 3850 1416 l 3839 1416 l 3831 1417 l 3825 1419 l 3819 1421 l 3811 1422 l 3800 1424 l 3786 1424 l 3769 1425 l 3750 1425 l 3726 1425 l 3712 1425 l 3707 1425 l 3706 1425 l 3703 1425 l 3692 1425 l 3675 1425 l 3658 1425 l 3646 1425 l 3640 1425 l 3638 1425 l 3635 1425 l 3629 1425 l 3617 1425 l 3600 1425 l 3583 1425 l 3571 1425 l 3565 1425 l 3563 1425 l 3560 1425 l 3554 1425 l 3542 1425 l 3525 1425 l 3508 1425 l 3496 1425 l 3490 1425 l 3488 1425 l 3485 1425 l 3479 1425 l 3467 1425 l 3450 1425 l 3433 1425 l 3421 1425 l 3415 1425 l 3413 1425 l 3410 1425 l 3404 1425 l 3392 1425 l 3375 1425 l 3358 1425 l 3346 1425 l 3340 1425 l 3338 1425 l 3335 1425 l 3329 1425 l 3317 1425 l 3300 1425 l 3283 1425 l 3271 1426 l 3265 1429 l 3263 1431 l 3260 1434 l 3254 1434 l 3242 1432 l 3225 1425 l 3211 1417 l 3200 1408 l 3193 1400 l 3189 1393 l 3187 1387 l 3186 1382 l 3182 1375 l 3175 1367 l 3164 1358 l 3150 1350 l 3133 1343 l 3121 1341 l 3115 1341 l 3113 1344 l 3110 1346 l 3104 1349 l 3092 1350 l 3075 1350 l 3058 1350 l 3047 1350 l 3044 1350 l 3043 1350 l 3038 1350 l 3024 1350 l 3000 1350 l 2981 1350 l 2964 1350 l 2950 1350 l 2939 1350 l 2931 1350 l 2925 1350 l 2919 1350 l 2911 1350 l 2900 1350 l 2886 1350 l 2869 1350 l 2850 1350 l 2826 1350 l 2812 1350 l 2807 1350 l 2806 1350 l 2803 1350 l 2792 1350 l 2775 1350 l 2758 1350 l 2746 1350 l 2740 1350 l 2738 1350 l 2735 1350 l 2729 1350 l 2717 1350 l 2700 1350 l 2683 1350 l 2671 1350 l 2665 1350 l 2663 1350 l 2660 1350 l 2654 1350 l 2642 1350 l 2625 1350 l 2608 1350 l 2596 1350 l 2590 1350 l 2588 1350 l 2585 1350 l 2579 1350 l 2567 1350 l 2550 1350 l 2533 1350 l 2521 1350 l 2515 1350 l 2513 1350 l 2510 1350 l 2504 1350 l 2492 1350 l 2475 1350 l 2458 1350 l 2446 1350 l 2440 1350 l 2438 1350 l 2435 1350 l 2429 1350 l 2417 1350 l 2400 1350 l 2383 1350 l 2371 1350 l 2365 1350 l 2363 1350 l 2360 1350 l 2354 1350 l 2342 1350 l 2325 1350 l 2307 1350 l 2295 1349 l 2287 1346 l 2281 1344 l 2276 1341 l 2270 1341 l 2260 1343 l 2250 1350 l 2243 1361 l 2242 1371 l 2245 1380 l 2250 1388 l 2255 1395 l 2258 1404 l 2257 1414 l 2250 1425 l 2240 1432 l 2230 1434 l 2224 1434 l 2219 1431 l 2213 1429 l 2205 1426 l 2193 1425 l 2175 1425 l 2157 1425 l 2145 1424 l 2137 1421 l 2131 1419 l 2126 1416 l 2120 1416 l 2110 1418 l 2100 1425 l 2093 1436 l 2092 1446 l 2095 1455 l 2100 1463 l 2105 1470 l 2108 1479 l 2107 1489 l 2100 1500 l 2090 1507 l 2080 1509 l 2074 1509 l 2069 1506 l 2063 1504 l 2055 1501 l 2043 1500 l 2025 1500 l 2008 1500 l 1996 1500 l 1990 1500 l 1988 1500 l 1985 1500 l 1979 1500 l 1967 1500 l 1950 1500 l 1933 1500 l 1921 1500 l 1915 1500 l 1913 1500 l 1910 1500 l 1904 1500 l 1892 1500 l 1875 1500 l 1858 1500 l 1846 1500 l 1840 1500 l 1838 1500 l 1835 1500 l 1829 1500 l 1817 1500 l 1800 1500 l 1783 1500 l 1771 1500 l 1765 1500 l 1763 1500 l 1760 1500 l 1754 1500 l 1742 1500 l 1725 1500 l 1707 1500 l 1695 1499 l 1687 1496 l 1681 1494 l 1676 1491 l 1670 1491 l 1660 1493 l 1650 1500 l 1644 1508 l 1640 1517 l 1639 1525 l 1638 1532 l 1638 1538 l 1638 1543 l 1639 1550 l 1640 1558 l 1644 1567 l 1650 1575 l 1661 1582 l 1671 1584 l 1680 1584 l 1688 1581 l 1695 1579 l 1704 1576 l 1714 1575 l 1725 1575 l 1727 1575 l 1728 1575 l 1730 1575 l 1731 1575 l 1732 1575 l 1733 1575 l 1734 1575 l 1735 1575 l 1736 1575 l 1737 1575 l 1736 1575 l 1735 1575 l 1734 1575 l 1733 1575 l 1732 1575 l 1731 1575 l 1730 1575 l 1728 1575 l 1727 1575 l 1725 1575 l 1715 1575 l 1705 1575 l 1699 1575 l 1694 1575 l 1688 1575 l 1680 1575 l 1668 1575 l cp gs col0 s gr % Polyline 7.500 slw [60] 0 sd n 6000 1200 m 12000 1200 l 12000 7200 l 6000 7200 l cp gs col0 s gr [] 0 sd $F2psEnd rs %%EndDocument endTexFig 385 4502 a Fu(jM)519 4516 y Fs(N)s(;K)686 4502 y Fu(\000)20 b Fv(m)857 4469 y Ft(\003)897 4502 y Fu(j)25 b Fr(6)g Fv(\020)78 4691 y FA(+)1684 4313 y Fv(K)1684 5046 y(K)1768 5013 y Fs(\013)2511 4384 y Fv(d)g Fr(>)g FA(2)656 5466 y FD(Figure)j(1.)38 b FE(Coarse)27 b(grained)g(con\014guration)f(with)g (o)n(v)n(erlapping)g(+)f(go)r(o)r(d)i(blo)r(c)n(ks.)p eop %%Page: 9 9 9 8 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)782 b(9)218 366 y FA(F)-8 b(or)39 b(large)g(mesoscopic) h(b)s(o)m(xes,)h(the)e(t)m(ypical)g(spin)e(con\014gurations)h(o)s(ccur) h(with)e(o)m(v)m(erwhelming)118 474 y(probabilit)m(y)-8 b(.)118 649 y FF(Theorem)34 b(3.1.)42 b Fn(L)-5 b(et)33 b Fv(\014)38 b Fn(b)-5 b(e)32 b(in)h Fj(B)p Fn(.)42 b(Then)33 b(for)g(any)g Fv(\020)f(>)25 b FA(0)p Fn(,)33 b(the)g(fol)5 b(lowing)34 b(holds)g(uniformly)g(in)e Fv(N)324 838 y Fu(8f)p Fv(x)472 852 y Fx(1)511 838 y Fv(;)15 b(:)g(:)g(:)i(;)e(x)765 853 y Fs(`)798 838 y Fu(g)26 b(2)962 815 y Fq(b)955 838 y Fy(D)1014 852 y Fs(N)s(;K)1167 838 y Fv(;)109 b(\026)1356 800 y Fx(+)1356 868 y Fs(\014)s(;N)1500 737 y Fq(\020)1555 838 y Fv(u)1607 794 y Fs(\020)1607 867 y(N)s(;K)1754 838 y FA(\()p Fv(x)1841 852 y Fx(1)1881 838 y FA(\))25 b(=)g(0)p Fv(;)15 b(:)g(:)g(:)i(;)e(u)2336 794 y Fs(\020)2336 867 y(N)s(;K)2484 838 y FA(\()p Fv(x)2571 853 y Fs(`)2604 838 y FA(\))26 b(=)f(0)2806 737 y Fq(\021)2901 838 y Fr(6)2997 765 y Fq(\000)3039 838 y Fv(\032)3086 794 y Fs(\020)3086 867 y(K)3154 765 y Fq(\001)3196 787 y Fs(`)3244 838 y Fv(;)206 b FA(\(3.2\))118 1055 y Fn(wher)-5 b(e)34 b(the)f(p)-5 b(ar)g(ameter)35 b Fv(\032)1000 1011 y Fs(\020)1000 1084 y(K)1101 1055 y Fn(vanishes)f(as)f Fv(K)39 b Fn(go)-5 b(es)33 b(to)g(in\014nity.)218 1229 y FA(Notice)j(that)g(the)f (mesoscopic)h(phase)f(lab)s(els)e(are)j(far)f(from)g(b)s(eing)f(indep)s (enden)m(t)f(v)-5 b(ariables.)54 b(In)118 1345 y(particular,)22 b(the)h(enlarged)e(b)s(oundaries)f(of)i(t)m(w)m(o)i(neigh)m(b)s(oring)c (b)s(o)m(xes)i(in)2608 1321 y Fq(b)2601 1345 y Fy(D)2660 1359 y Fs(N)s(;K)2835 1345 y FA(o)m(v)m(erlap.)39 b(This)20 b(implies)118 1453 y(that)33 b(t)m(w)m(o)h(neigh)m(b)s(oring)d(b)s(o)m (xes)h(cannot)h(b)s(e)f(lab)s(elled)e(b)m(y)j(opp)s(osite)f(signs.)46 b(Let)33 b(us)f(\014rst)g(dra)m(w)g(some)118 1560 y(consequences)22 b(of)f(this)g(construction.)37 b(The)21 b(pro)s(of)f(of)i(Theorem)f (3.1)h(is)e(p)s(ostp)s(oned)g(to)i(the)g(App)s(endix.)218 1728 y(This)36 b(coarse)j(graining)e(describ)s(es)g(the)h(lo)s(cal)f (order)h(parameter.)65 b(Giv)m(en)38 b(an)m(y)h Fv(\016)j(>)c FA(0,)j(one)d(can)118 1836 y(c)m(ho)s(ose)31 b(the)f(accuracy)h Fv(\020)37 b FA(of)30 b(the)g(coarse)h(graining)e(and)g(a)h(scale)h Fv(K)2447 1850 y Fx(0)2486 1836 y FA(\()p Fv(\016)n(;)15 b(\014)5 b FA(\))32 b(suc)m(h)e(that)h(for)e(an)m(y)i(meso-)118 1943 y(scopic)f Fv(K)i Fr(>)25 b Fv(K)668 1957 y Fx(0)775 2149 y FA(lim)736 2209 y Fs(N)7 b Ft(!1)1075 2087 y FA(1)p 991 2128 214 4 v 991 2211 a Fv(N)1074 2185 y Fs(d)p Ft(\000)p Fx(1)1230 2149 y FA(log)16 b Fv(\026)1417 2111 y Fx(+)1417 2178 y Fs(\014)s(;N)1562 2048 y Fq(\020)1616 2149 y Fu(kM)1770 2163 y Fs(N)s(;K)1938 2149 y Fu(\000)k Fv(m)2109 2111 y Ft(\003)2109 2172 y Fs(\014)2156 2149 y Fv(u)2208 2105 y Fs(\020)2208 2177 y(N)s(;K)2355 2149 y Fu(k)2400 2163 y Fx(1)2465 2149 y Fv(>)25 b(\016)2604 2048 y Fq(\021)2715 2149 y FA(=)55 b Fu(\0001)15 b Fv(:)432 b FA(\(3.3\))218 2354 y(In)29 b(order)h(to)h(c)m(hec)m(k)h(this)e(assertion,)g(w)m(e)h (\014rst)e(notice)i(that)g(the)g(prop)s(ert)m(y)e FF(\(P2\))i FA(implies)862 2585 y Fu(kM)1016 2599 y Fs(N)s(;K)1184 2585 y Fu(\000)19 b Fv(m)1354 2547 y Ft(\003)1394 2585 y Fv(u)1446 2541 y Fs(\020)1446 2614 y(N)s(;K)1593 2585 y Fu(k)1638 2599 y Fx(1)1733 2585 y Fr(6)30 b Fv(\020)d FA(+)2002 2523 y(2)p Fv(K)2131 2491 y Fs(d)p 2002 2564 170 4 v 2025 2647 a Fv(N)2108 2621 y Fs(d)2262 2499 y Fq(X)2197 2715 y Fs(x)p Ft(2)2288 2698 y Fk(b)2284 2715 y Fo(D)2325 2726 y Fp(N)s(;K)2474 2585 y FA(1)2519 2621 y Fs(u)2560 2588 y Fp(\020)2560 2644 y(N)r(;K)2689 2621 y Fx(\()p Fs(x)p Fx(\)=0)2893 2585 y Fv(:)118 2876 y FA(This)i(estimate)i(com)m(bined)e(with)g(Theorem)i(3.1)g(leads)f(to) 341 3157 y Fv(\026)396 3119 y Fx(+)396 3186 y Fs(\014)s(;N)541 3056 y Fq(\020)596 3157 y Fu(kM)750 3171 y Fs(N)s(;K)917 3157 y Fu(\000)20 b Fv(m)1088 3120 y Ft(\003)1128 3157 y Fv(u)1180 3113 y Fs(\020)1180 3186 y(N)s(;K)1327 3157 y Fu(k)1372 3171 y Fx(1)1437 3157 y Fv(>)25 b(\016)1576 3056 y Fq(\021)1656 3157 y Fr(6)30 b Fv(\026)1812 3119 y Fx(+)1812 3186 y Fs(\014)s(;N)1957 2947 y Fq(0)1957 3107 y(B)1957 3165 y(@)2156 3096 y FA(1)p 2047 3136 264 4 v 2047 3236 a Fu(j)2080 3213 y Fq(b)2072 3236 y Fy(D)2131 3250 y Fs(N)t(;K)2285 3236 y Fu(j)2401 3071 y Fq(X)2335 3287 y Fs(x)p Ft(2)2426 3270 y Fk(b)2422 3287 y Fo(D)2464 3298 y Fp(N)r(;K)2613 3157 y FA(1)2658 3193 y Fs(u)2699 3160 y Fp(\020)2699 3216 y(N)r(;K)2827 3193 y Fx(\()p Fs(x)p Fx(\)=0)3041 3157 y Fv(>)3147 3096 y(\016)24 b Fu(\000)c Fv(\020)p 3147 3136 202 4 v 3225 3219 a FA(2)3359 2947 y Fq(1)3359 3107 y(C)3359 3165 y(A)1656 3520 y Fr(6)40 b FA(exp)1921 3364 y Fq( )1993 3520 y Fu(\000)p Fv(c)2103 3534 y Fx(1)2153 3458 y Fv(N)2236 3425 y Fs(d)p 2153 3499 125 4 v 2153 3582 a Fv(K)2237 3556 y Fs(d)2302 3520 y FA(log)2435 3364 y Fq( )2517 3458 y Fv(\016)24 b Fu(\000)c Fv(\020)p 2517 3499 202 4 v 2537 3600 a FA(2)p Fv(\032)2629 3556 y Fs(\020)2629 3629 y(K)2728 3364 y Fq(!!)2887 3520 y Fv(:)218 3769 y FA(According)31 b(to)i(estimate)f(\(3.3\))h(the)f(lo) s(cal)f(a)m(v)m(eraged)j(magnetization)e(can)g(b)s(e)f(con)m(trolled)h (b)m(y)f(the)118 3877 y(mesoscopic)g(phase)f(lab)s(els)e(and)i(in)f (particular)g(the)h(Prop)s(osition)f(3.1)i(follo)m(ws)f(from)118 4051 y FF(Theorem)35 b(3.2.)42 b Fn(L)-5 b(et)34 b Fv(\014)39 b Fn(b)-5 b(e)33 b(in)g Fj(B)h Fn(and)g Fv(\020)f(>)26 b FA(0)p Fn(.)44 b(F)-7 b(or)35 b(every)e Fv(a)26 b(>)h FA(0)33 b Fn(and)i Fv(\016)30 b(>)c FA(0)34 b Fn(ther)-5 b(e)34 b(exists)g(a)f(\014nite)118 4159 y(sc)-5 b(ale)33 b Fv(K)413 4173 y Fx(0)453 4159 y FA(\()p Fv(\016)s FA(\))p Fn(,)h(such)f(that)h(for)f(al)5 b(l)33 b Fv(K)f Fr(>)25 b Fv(K)1578 4173 y Fx(0)765 4369 y FA(lim)15 b(sup)802 4448 y Fs(N)7 b Ft(!1)1152 4308 y FA(1)p 1068 4348 214 4 v 1068 4432 a Fv(N)1151 4405 y Fs(d)p Ft(\000)p Fx(1)1307 4369 y FA(log)17 b Fv(\026)1495 4331 y Fx(+)1495 4399 y Fs(\014)s(;N)1624 4268 y Fq(\020)1679 4369 y Fv(u)1731 4325 y Fs(\020)1731 4398 y(N)s(;K)1903 4369 y Fu(62)25 b(V)7 b FA(\()p Fu(C)2135 4383 y Fs(a)2177 4369 y Fv(;)15 b FA(2)p Fv(\016)s FA(\))2340 4268 y Fq(\021)2421 4369 y Fr(6)53 b Fu(\000)20 b Fv(c)p FA(\()p Fv(\014)5 b(;)15 b(K)7 b FA(\))p Fv(a)15 b(;)462 b FA(\(3.4\))118 4592 y Fn(wher)-5 b(e)34 b Fv(c)p FA(\()p Fv(\014)5 b(;)15 b(K)7 b FA(\))34 b Fn(is)e(a)h(p)-5 b(ositive)34 b(c)-5 b(onstant.)218 4767 y FA(This)26 b(theorem)i(amoun)m(ts)g(to)g(con)m (trol)h(the)e(phase)h(of)g(the)g(small)e(con)m(tours,)j(i.e.)40 b(to)28 b(pro)m(v)m(e)h(that)f(the)118 4874 y(macroscopic)34 b(phase)f(separation)g(is)f(the)h(optimal)f(scenario)i(to)f(shift)f (the)i(magnetization)g(whereas)118 4982 y(the)k(creation)h(of)f(man)m (y)g(small)f(droplets)g(do)s(es)h(not)g(con)m(tribute.)64 b(The)37 b(ab)s(o)m(v)m(e)j(theorem)e(has)g(b)s(een)118 5090 y(deriv)m(ed)30 b(in)g([BIV1)q(])i(in)d(an)j(abstract)g(setting)f (\(see)h(also)f([BBP)q(]\).)44 b(As)31 b(the)g(coarse)h(graining)e (satis\014es)118 5198 y(the)h(h)m(yp)s(otheses)f(of)g(Theorem)g(2.2.1)j (of)d([BIV1)q(],)h(the)g(conclusion)e(follo)m(ws.)118 5372 y FF(Remark)g(3.1.)39 b Fn(It)28 b(should)i(b)-5 b(e)28 b(note)-5 b(d)30 b(that)g(in)e(the)h(pr)-5 b(o)g(of)30 b(of)f FA([BIV1)q(])f Fn(the)h(BK)f(ine)-5 b(quality)29 b(was)h(invoke)-5 b(d)118 5480 y(but)32 b(a)h(Peierls)g(ine)-5 b(quality)33 b(for)g(the)g(c)-5 b(o)g(arse)35 b(gr)-5 b(aine)g(d)34 b(c)-5 b(ontours)34 b(is)f(su\016cient.)p eop %%Page: 10 10 10 9 bop 118 45 a Fx(10)1460 b(T.)23 b(BODINEA)n(U)218 366 y FA(As)36 b(noticed)g(in)f([BIV2)q(],)j(a)f(theorem)g(similar)d (to)j(Theorem)f(3.2)h(can)g(also)f(b)s(e)f(stated)j(for)e(phase)118 474 y(lab)s(els)d(taking)i(a)h(\014nite)e(n)m(um)m(b)s(er)g(of)h(v)-5 b(alues.)54 b(Th)m(us,)36 b(similar)c(results)i(\(coarse)j(graining,)e (exp)s(onen-)118 582 y(tial)h(tigh)m(tness\))i(should)d(b)s(e)h(v)-5 b(alid)36 b(as)h(w)m(ell)f(for)h(m)m(ulti-phase)f(mo)s(dels)g(whic)m(h) f(satisfy)i(P)m(eierls)f(t)m(yp)s(e)118 690 y(estimates.)118 959 y(3.2.)47 b FF(Equilibrium)36 b(crystal)h(shap)s(es.)45 b FA(W)-8 b(e)33 b(are)f(going)g(to)g(pro)m(v)m(e)h(the)f(analogue)g (of)g(Theorem)f(2.3)118 1067 y(for)f(the)h(Ising)f(mo)s(del)f(at)j(lo)m (w)e(temp)s(erature.)41 b(The)30 b(pro)s(of)g(relies)g(on)g(the)h (previous)e(coarse)j(graining.)118 1175 y(Nev)m(ertheless,)i(it)f(also) g(uses)f(mo)s(del)g(dep)s(enden)m(t)g(argumen)m(ts,)i(namely)e(the)h (spin)e(\015ip)g(symmetry)h(of)118 1282 y(the)f(Ising)e(mo)s(del)g(and) h(the)g(existence)h(of)g(the)f(surface)h(tension.)118 1475 y FF(Theorem)k(3.3.)43 b Fn(L)-5 b(et)33 b Fv(\014)39 b Fn(b)-5 b(e)33 b(in)g Fu(B)j Fn(and)e Fv(m)f Fn(b)-5 b(e)34 b(in)f FA(])21 b Fu(\000)f Fv(m)2067 1442 y Ft(\003)2067 1502 y Fs(\014)2114 1475 y Fv(;)15 b(m)2234 1442 y Ft(\003)2234 1502 y Fs(\014)2282 1475 y FA([)p Fn(.)44 b(F)-7 b(or)34 b(every)g Fv(\016)c(>)c FA(0)p Fn(,)34 b(one)g(c)-5 b(an)34 b(cho)-5 b(ose)118 1592 y(a)33 b(sc)-5 b(ale)33 b Fv(K)492 1606 y Fx(0)557 1592 y FA(=)25 b Fv(K)730 1606 y Fx(0)770 1592 y FA(\()p Fv(\014)5 b(;)15 b(\016)s FA(\))35 b Fn(such)d(that)i (for)g(any)f Fv(K)f Fr(>)25 b Fv(K)2008 1606 y Fx(0)701 1846 y FA(lim)662 1906 y Fs(N)7 b Ft(!1)906 1846 y Fv(\026)961 1807 y Fx(+)961 1875 y Fs(\014)s(;N)1106 1718 y Fq(\022)1216 1846 y FA(inf)1173 1906 y Fs(v)r Ft(2D)1311 1914 y Fp(m)1385 1846 y Fu(kM)1539 1860 y Fs(N)s(;K)1707 1846 y Fu(\000)20 b Fv(m)1878 1808 y Ft(\003)1878 1869 y Fs(\014)1925 1846 y Fv(v)s Fu(k)2017 1860 y Fx(1)2082 1846 y Fr(6)25 b Fv(\016)2255 1741 y Fq(\014)2255 1796 y(\014)2255 1850 y(\014)2310 1846 y FF(M)2409 1860 y Fs(N)2502 1846 y Fr(6)g Fv(m)2678 1718 y Fq(\023)2770 1846 y FA(=)g(1)15 b Fv(:)218 2093 y FA(This)34 b(theorem)j(holds)d(also)i(for)g(a)h (larger)f(range)g(of)h(temp)s(eratures)e(\([CePi1)q(,)h(BIV1)q(]\),)i (where)e Fu(B)118 2201 y FA(is)30 b(the)g(domain)g(of)g(v)-5 b(alidit)m(y)29 b(of)i(Pisztora's)g(coarse)g(graining)e([Pi].)41 b(It)30 b(is)g(actually)g(conjectured)h(that)118 2309 y Fu(B)d FA(=])p Fv(\014)353 2323 y Fs(c)388 2309 y Fv(;)15 b Fu(1)p FA([.)218 2508 y(The)32 b(concen)m(tration)j(in)d Fy(L)1142 2475 y Fx(1)1221 2508 y FA(of)h Fu(M)1436 2522 y Fs(N)s(;K)1616 2508 y FA(to)h(the)g(solutions)d(of)j(the)f(v)-5 b(ariational)32 b(problem)g(requires)118 2616 y(the)37 b(deriv)-5 b(ation)36 b(of)h(precise)g(logarithmic)f(asymptotic.)61 b(More)38 b(precisely)-8 b(,)38 b(w)m(e)f(are)h(going)f(to)h(c)m(hec)m (k)118 2731 y(that)33 b(the)g(probabilit)m(y)e(that)i Fu(M)1252 2745 y Fs(N)s(;K)1432 2731 y FA(is)f(close)h(to)g(a)g (con\014guration)f Fv(m)2570 2698 y Ft(\003)2570 2758 y Fs(\014)2617 2731 y Fv(v)k FA(\(with)c Fv(v)h Fu(2)28 b FA(BV)r(\()3285 2707 y Fq(b)3277 2731 y Fy(D)23 b Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))r(\))118 2859 y(deca)m(ys)31 b(exp)s(onen)m(tially)e(with)g(a)i(surface)f(order)g Fv(N)1877 2826 y Fs(d)p Ft(\000)p Fx(1)2008 2859 y Fu(W)2098 2874 y Fs(\014)2145 2859 y FA(\()p Fv(v)s FA(\).)118 3068 y FF(Prop)s(osition)53 b(3.2.)d Fn(L)-5 b(et)46 b Fv(\014)k Fn(b)-5 b(e)46 b(in)g Fj(B)f Fn(and)i(let)f Fv(v)j Fn(b)-5 b(e)45 b(in)h FA(BV)r(\()2408 3045 y Fq(b)2400 3068 y Fy(D)23 b Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))r Fn(,)48 b(then)f(one)f(c)-5 b(an)46 b(cho)-5 b(ose)118 3176 y Fv(\016)158 3190 y Fx(0)223 3176 y FA(=)25 b Fv(\016)359 3190 y Fx(0)399 3176 y FA(\()p Fv(v)s FA(\))p Fn(,)33 b(such)g(that)h(uniformly)g(in)e Fv(\016)d(<)c(\016)1701 3190 y Fx(0)519 3418 y FA(lim)15 b(inf)543 3479 y Fs(N)7 b Ft(!1)905 3357 y FA(1)p 821 3398 214 4 v 821 3481 a Fv(N)904 3455 y Fs(d)p Ft(\000)p Fx(1)1060 3418 y FA(log)16 b Fv(\026)1247 3380 y Fx(+)1247 3448 y Fs(\014)s(;N)1377 3345 y Fq(\000)1419 3418 y Fu(kM)1573 3432 y Fs(N)s(;K)1741 3418 y Fu(\000)j Fv(m)1911 3381 y Ft(\003)1911 3442 y Fs(\014)1958 3418 y Fv(v)s Fu(k)2050 3432 y Fx(1)2116 3418 y Fr(6)25 b Fv(\016)2255 3345 y Fq(\001)2323 3418 y Fr(>)45 b Fu(\000)20 b(W)2620 3433 y Fs(\014)2667 3418 y FA(\()p Fv(v)s FA(\))h Fu(\000)f Fv(o)p FA(\()p Fv(\016)s FA(\))15 b Fv(;)118 3656 y Fn(wher)-5 b(e)34 b(the)f(function)g Fv(o)p FA(\()p Fu(\001)p FA(\))g Fn(dep)-5 b(ends)34 b(only)g(on)f Fv(\014)38 b Fn(and)33 b Fv(v)j Fn(and)e(vanishes)f(as)g Fv(\016)k Fn(go)-5 b(es)33 b(to)g(0.)118 4036 y FF(Prop)s(osition)e (3.3.)39 b Fn(L)-5 b(et)29 b Fv(\014)k Fn(b)-5 b(e)29 b(in)f Fj(B)p Fn(.)41 b(F)-7 b(or)30 b(al)5 b(l)29 b Fv(v)j Fn(in)c FA(BV)r(\()2132 4012 y Fq(b)2124 4036 y Fy(D)23 b Fv(;)15 b Fu(f\006)p FA(1)p Fu(g)p FA(\))30 b Fn(such)f(that)h Fu(W)2976 4051 y Fs(\014)3023 4036 y FA(\()p Fv(v)s FA(\))f Fn(is)g(\014nite,)g(one)118 4143 y(c)-5 b(an)33 b(cho)-5 b(ose)34 b Fv(\016)613 4157 y Fx(0)679 4143 y FA(=)25 b Fv(\016)815 4157 y Fx(0)854 4143 y FA(\()p Fv(v)s FA(\))p Fn(,)34 b(such)f(that)g(uniformly)h(in)f Fv(\016)c(<)c(\016)2157 4157 y Fx(0)506 4386 y FA(lim)15 b(sup)543 4464 y Fs(N)7 b Ft(!1)918 4324 y FA(1)p 834 4365 V 834 4448 a Fv(N)917 4422 y Fs(d)p Ft(\000)p Fx(1)1073 4386 y FA(log)16 b Fv(\026)1260 4347 y Fx(+)1260 4415 y Fs(\014)s(;N)1390 4312 y Fq(\000)1432 4386 y Fu(kM)1586 4400 y Fs(N)s(;K)1754 4386 y Fu(\000)k Fv(m)1925 4348 y Ft(\003)1925 4409 y Fs(\014)1972 4386 y Fv(v)s Fu(k)2064 4400 y Fx(1)2129 4386 y Fr(6)25 b Fv(\016)2268 4312 y Fq(\001)2336 4386 y Fr(6)45 b Fu(\000)20 b(W)2633 4401 y Fs(\014)2680 4386 y FA(\()p Fv(v)s FA(\))h(+)f Fv(o)p FA(\()p Fv(\016)s FA(\))15 b Fv(;)118 4640 y Fn(wher)-5 b(e)34 b(the)f(function)g Fv(o)p FA(\()p Fu(\001)p FA(\))g Fn(dep)-5 b(ends)34 b(only)g(on)f Fv(\014)38 b Fn(and)33 b Fv(v)j Fn(and)e(vanishes)f(as)g Fv(\016)k Fn(go)-5 b(es)33 b(to)g(0.)218 4833 y FA(Theorem)h(3.3)i(can)f(b)s(e)g(obtained) f(b)m(y)h(com)m(bining)e(Prop)s(ositions)g(3.1,)k(3.2,)g(3.3.)56 b(W)-8 b(e)36 b(recall)e(that)118 4941 y Fu(C)166 4955 y Fs(a)237 4941 y FA(is)28 b(compact)j(with)d(resp)s(ect)h(to)h(the)f Fy(L)1526 4908 y Fx(1)1600 4941 y FA(top)s(ology)h(\(see)g([EG)q(]\).) 41 b(Th)m(us)28 b(the)h(exp)s(onen)m(tial)f(tigh)m(tness)118 5049 y(prop)s(ert)m(y)f(3.1)h(enables)e(us)h(to)h(fo)s(cus)e(only)g(on) h(a)h(\014nite)e(n)m(um)m(b)s(er)g(of)h(con\014gurations)f(close)i(to)g Fu(C)3399 5063 y Fs(a)3440 5049 y FA(.)40 b(The)118 5157 y(precise)31 b(asymptotic)i(of)f(these)g(con\014gurations)f(is)g(then)h (estimated)g(b)m(y)g(Prop)s(ositions)e(3.2,)j(3.3)g(\(see)118 5264 y([B1)q(])e(for)f(details\).)218 5372 y(In)38 b(the)h(follo)m (wing)f(sections,)j(Prop)s(ositions)c(3.2,)43 b(3.3)d(are)f(implemen)m (ted)f(in)g(the)h(framew)m(ork)g(of)118 5480 y(nearest)31 b(neigh)m(b)s(or)e(Ising)g(mo)s(del)g(at)j(lo)m(w)e(temp)s(erature.)p eop %%Page: 11 11 11 10 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(11)118 366 y FA(3.3.)47 b FF(Lo)m(w)m(er)26 b(b)s(ound.)46 b FA(In)23 b(order)g(to)g(deriv)m(e)g(Prop)s(osition)e (3.2,)26 b(it)d(is)f(enough)h(to)h(consider)e(the)i(t)m(ypical)118 474 y(spin)k(con\014gurations)h(whic)m(h)f(con)m(tain)j(a)f (microscopic)f(con)m(tour)h(in)f(a)h(neigh)m(b)s(orho)s(o)s(d)d(of)j (the)g(b)s(ound-)118 582 y(ary)g(of)h Fv(@)434 549 y Ft(\003)474 582 y Fv(v)s FA(.)118 798 y Fn(Step)i(1)g(:)42 b(Appr)-5 b(oximation)36 b(pr)-5 b(o)g(c)g(e)g(dur)g(e.)p 118 830 1366 4 v 218 931 a FA(W)d(e)23 b(\014rst)e(start)h(b)m(y)g (appro)m(ximating)f(the)h(b)s(oundary)d Fv(@)2071 898 y Ft(\003)2111 931 y Fv(v)25 b FA(b)m(y)d(a)g(regular)f(surface)h Fv(@)3027 908 y Fq(b)3016 931 y Fv(V)e FA(.)38 b(A)22 b(p)s(olyhedral)118 1039 y(set)31 b(has)f(a)g(b)s(oundary)f(included)e (in)i(the)h(union)f(of)h(a)g(\014nite)g(n)m(um)m(b)s(er)e(of)j(h)m(yp)s (er-planes.)39 b(The)29 b(surface)118 1147 y Fv(@)171 1114 y Ft(\003)211 1147 y Fv(v)k FA(can)e(b)s(e)f(appro)m(ximated)g(as) h(follo)m(ws)e(\(see)i(\014gure)f(2\))118 1329 y FF(Theorem)k(3.4.)42 b Fn(F)-7 b(or)34 b(any)f Fv(\016)j Fn(p)-5 b(ositive,)34 b(ther)-5 b(e)33 b(exists)g(a)g(p)-5 b(olyhe)g(dr)g(al)37 b(set)2671 1306 y Fq(b)2660 1329 y Fv(V)53 b Fn(such)32 b(that)900 1496 y Fu(k)p FA(1)-25 b(I)1008 1513 y Fk(b)999 1530 y Fs(V)1080 1496 y Fu(\000)20 b Fv(v)s Fu(k)1263 1510 y Fx(1)1329 1496 y Fr(6)k Fv(\016)190 b FA(and)1986 1419 y Fq(\014)1986 1473 y(\014)2017 1496 y Fu(W)2107 1511 y Fs(\014)2154 1496 y FA(\()2200 1473 y Fq(b)2189 1496 y Fv(V)20 b FA(\))h Fu(\000)f(W)2499 1511 y Fs(\014)2546 1496 y FA(\()p Fv(v)s FA(\))2663 1419 y Fq(\014)2663 1473 y(\014)2719 1496 y Fr(6)25 b Fv(\016)n(:)118 1679 y Fn(F)-7 b(or)27 b(any)e Fv(h)h Fn(smal)5 b(l)26 b(enough)g(ther)-5 b(e)26 b(ar)-5 b(e)27 b Fv(`)e Fn(disjoint)h(p)-5 b(ar)g(al)5 b(lelepip)-5 b(e)g(ds)2417 1656 y Fq(b)2400 1679 y Fv(R)2470 1646 y Fx(1)2509 1679 y Fv(;)15 b(:)g(:)g(:)h(;)2728 1656 y Fq(b)2710 1679 y Fv(R)2780 1646 y Fs(`)2839 1679 y Fn(with)26 b(b)-5 b(asis)3259 1656 y Fq(b)3240 1679 y Fv(B)3314 1646 y Fx(1)3353 1679 y Fv(;)15 b(:)g(:)g(:)i(;)3574 1656 y Fq(b)3555 1679 y Fv(B)3629 1646 y Fs(`)118 1794 y Fn(include)-5 b(d)31 b(in)f Fv(@)644 1771 y Fq(b)633 1794 y Fv(V)50 b Fn(of)30 b(side)g(length)h Fv(h)f Fn(and)h(height)f Fv(\016)s(h)p Fn(.)42 b(F)-7 b(urthermor)i(e,)33 b(the)d(sets)2867 1771 y Fq(b)2848 1794 y Fv(B)2922 1761 y Fx(1)2961 1794 y Fv(;)15 b(:)g(:)g(:)i(;)3182 1771 y Fq(b)3163 1794 y Fv(B)3237 1761 y Fs(`)3299 1794 y Fn(c)-5 b(over)31 b Fv(@)3600 1771 y Fq(b)3588 1794 y Fv(V)118 1908 y Fn(up)i(to)g(a)g (set)g(of)g(me)-5 b(asur)g(e)34 b(less)f(than)g Fv(\016)k Fn(denote)-5 b(d)34 b(by)1954 1885 y Fq(b)1940 1908 y Fv(U)2012 1875 y Fs(\016)2075 1908 y FA(=)25 b Fv(@)2236 1885 y Fq(b)2224 1908 y Fv(V)41 b Fu(n)2384 1840 y Fq(S)2460 1866 y Fs(`)2460 1935 y(i)p Fx(=1)2612 1885 y Fq(b)2593 1908 y Fv(B)2667 1875 y Fs(i)2727 1908 y Fn(and)34 b(they)f(satisfy) 1061 2060 y Fq(\014)1061 2115 y(\014)1061 2170 y(\014)1157 2051 y Fs(`)1106 2079 y Fq(X)1115 2274 y Fs(i)p Fx(=1)1253 2041 y Fq(Z)1318 2231 y Fk(b)1303 2247 y Fs(B)1359 2229 y Fp(i)1405 2165 y Fv(\034)1445 2180 y Fs(\014)1492 2165 y FA(\()n Fv(~)-43 b(n)1582 2179 y Fs(i)1610 2165 y FA(\))15 b Fv(d)p Fu(H)1785 2127 y Fx(\()p Fs(d)p Ft(\000)p Fx(1\))1784 2187 y Fs(x)1991 2165 y Fu(\000)20 b(W)2172 2180 y Fs(\014)2219 2165 y FA(\()p Fv(v)s FA(\))2336 2060 y Fq(\014)2336 2115 y(\014)2336 2170 y(\014)2393 2165 y Fr(6)25 b Fv(\016)n(;)118 2433 y Fn(wher)-5 b(e)34 b(the)f(normal)h(to)967 2410 y Fq(b)947 2433 y Fv(B)1021 2400 y Fs(i)1082 2433 y Fn(is)e(denote)-5 b(d)35 b(by)30 b Fv(~)-43 b(n)1685 2447 y Fs(i)1713 2433 y Fn(.)118 2603 y FA(The)31 b(pro)s(of)h(is)e(a)j(direct)e(application) f(of)i(Resh)m(tn)m(y)m(ak's)h(Theorem)f(and)f(can)h(b)s(e)f(found)g(in) f(the)i(pap)s(er)118 2711 y(of)f(Alb)s(erti,)d(Bellettini)h([AlBe].)730 2853 y 18553547 9323399 0 0 48481157 24273469 startTexFig 730 2853 a %%BeginDocument: ./pictures/approx_low.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: approx_low.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Mon Dec 18 15:58:35 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 737 369 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 369 moveto 0 0 lineto 737 0 lineto 737 369 lineto closepath clip newpath % Fill background color 0 0 moveto 737 0 lineto 737 369 lineto 0 369 lineto closepath 1.00 1.00 1.00 setrgbcolor fill -9.0 587.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline 7.500 slw gs clippath 6930 5010 m 6870 5010 l 6870 5195 l 6900 5045 l 6930 5195 l cp eoclip n 6900 5400 m 6900 5100 l 6900 5025 l gs col0 s gr gr % arrowhead n 6930 5195 m 6900 5045 l 6870 5195 l 6900 5165 l 6930 5195 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 2441 5473 m 2494 5502 l 2583 5340 l 2485 5458 l 2530 5311 l cp eoclip n 3375 3825 m 2475 5475 l gs col0 s gr gr % arrowhead n 2530 5311 m 2485 5458 l 2583 5340 l 2542 5352 l 2530 5311 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 9572 5719 m 9632 5709 l 9601 5527 l 9597 5680 l 9542 5536 l cp eoclip n 9300 3900 m 9600 5700 l gs col0 s gr gr % arrowhead n 9542 5536 m 9597 5680 l 9601 5527 l 9577 5561 l 9542 5536 l cp gs 0.00 setgray ef gr col0 s % Polyline 0.000 slw n 925 8750 m 928 8724 l 931 8698 l 934 8672 l 938 8645 l 941 8619 l 946 8592 l 950 8565 l 955 8537 l 961 8509 l 967 8481 l 973 8452 l 980 8423 l 987 8393 l 995 8363 l 1003 8333 l 1011 8303 l 1020 8273 l 1029 8243 l 1038 8213 l 1048 8183 l 1058 8153 l 1068 8123 l 1079 8093 l 1090 8062 l 1101 8031 l 1113 8000 l 1122 7974 l 1133 7947 l 1143 7920 l 1154 7892 l 1166 7863 l 1178 7833 l 1191 7802 l 1204 7771 l 1218 7739 l 1232 7706 l 1247 7672 l 1262 7638 l 1278 7603 l 1294 7568 l 1311 7532 l 1328 7497 l 1346 7461 l 1363 7425 l 1381 7389 l 1400 7354 l 1418 7319 l 1437 7285 l 1455 7251 l 1474 7217 l 1493 7185 l 1511 7153 l 1530 7121 l 1549 7091 l 1568 7061 l 1587 7032 l 1606 7003 l 1625 6975 l 1643 6949 l 1662 6923 l 1681 6897 l 1701 6872 l 1721 6846 l 1741 6820 l 1762 6795 l 1784 6769 l 1807 6744 l 1830 6718 l 1853 6692 l 1878 6667 l 1903 6641 l 1928 6616 l 1955 6590 l 1981 6565 l 2008 6541 l 2036 6516 l 2064 6492 l 2092 6468 l 2120 6445 l 2149 6422 l 2178 6400 l 2207 6378 l 2236 6357 l 2265 6336 l 2294 6316 l 2323 6296 l 2352 6277 l 2381 6258 l 2411 6240 l 2440 6222 l 2470 6205 l 2500 6188 l 2527 6172 l 2555 6157 l 2583 6142 l 2612 6127 l 2642 6112 l 2672 6096 l 2703 6081 l 2735 6066 l 2768 6051 l 2801 6036 l 2835 6021 l 2870 6005 l 2906 5990 l 2942 5975 l 2979 5960 l 3016 5945 l 3054 5930 l 3093 5916 l 3132 5901 l 3171 5887 l 3210 5873 l 3250 5860 l 3289 5846 l 3329 5833 l 3368 5820 l 3408 5808 l 3447 5796 l 3486 5784 l 3525 5773 l 3563 5762 l 3601 5752 l 3639 5741 l 3677 5732 l 3714 5722 l 3751 5713 l 3788 5704 l 3825 5696 l 3863 5688 l 3898 5680 l 3933 5672 l 3969 5665 l 4006 5658 l 4042 5651 l 4080 5644 l 4117 5637 l 4156 5631 l 4195 5624 l 4235 5618 l 4275 5612 l 4316 5605 l 4358 5599 l 4400 5593 l 4443 5588 l 4487 5582 l 4530 5576 l 4575 5571 l 4619 5566 l 4664 5560 l 4709 5555 l 4754 5551 l 4799 5546 l 4844 5541 l 4889 5537 l 4934 5533 l 4979 5529 l 5024 5525 l 5068 5521 l 5112 5517 l 5156 5514 l 5199 5510 l 5242 5507 l 5285 5504 l 5327 5501 l 5370 5498 l 5412 5495 l 5454 5493 l 5495 5490 l 5538 5488 l 5578 5485 l 5618 5483 l 5659 5480 l 5700 5478 l 5742 5476 l 5784 5473 l 5827 5471 l 5871 5469 l 5915 5467 l 5959 5465 l 6004 5462 l 6050 5460 l 6096 5458 l 6143 5456 l 6190 5454 l 6237 5453 l 6284 5451 l 6332 5449 l 6380 5447 l 6428 5446 l 6475 5444 l 6523 5443 l 6570 5442 l 6617 5441 l 6664 5439 l 6710 5438 l 6756 5438 l 6801 5437 l 6845 5436 l 6888 5436 l 6931 5435 l 6973 5435 l 7014 5435 l 7055 5434 l 7094 5434 l 7133 5435 l 7171 5435 l 7208 5435 l 7244 5436 l 7280 5436 l 7315 5437 l 7350 5438 l 7392 5439 l 7434 5440 l 7475 5441 l 7516 5443 l 7557 5445 l 7597 5447 l 7638 5449 l 7679 5452 l 7719 5454 l 7760 5457 l 7800 5460 l 7840 5463 l 7880 5467 l 7920 5470 l 7960 5474 l 7999 5478 l 8038 5482 l 8077 5486 l 8115 5490 l 8152 5495 l 8188 5499 l 8224 5504 l 8259 5509 l 8294 5513 l 8327 5518 l 8360 5523 l 8392 5528 l 8424 5533 l 8454 5538 l 8484 5543 l 8514 5548 l 8543 5552 l 8572 5557 l 8600 5563 l 8632 5568 l 8664 5574 l 8696 5580 l 8729 5586 l 8761 5593 l 8795 5599 l 8828 5606 l 8862 5613 l 8896 5620 l 8931 5628 l 8965 5635 l 9000 5643 l 9035 5651 l 9071 5659 l 9106 5668 l 9140 5676 l 9175 5685 l 9209 5693 l 9243 5702 l 9276 5711 l 9309 5720 l 9341 5729 l 9372 5738 l 9403 5746 l 9433 5755 l 9462 5764 l 9491 5773 l 9520 5782 l 9547 5791 l 9575 5800 l 9604 5810 l 9634 5820 l 9663 5831 l 9693 5841 l 9723 5852 l 9753 5864 l 9784 5876 l 9814 5888 l 9845 5901 l 9876 5914 l 9908 5928 l 9939 5942 l 9970 5957 l 10000 5971 l 10031 5986 l 10061 6001 l 10090 6016 l 10119 6032 l 10147 6047 l 10174 6063 l 10200 6078 l 10226 6094 l 10251 6109 l 10274 6125 l 10297 6140 l 10320 6156 l 10341 6172 l 10363 6188 l 10385 6205 l 10407 6223 l 10428 6241 l 10450 6260 l 10471 6279 l 10493 6299 l 10514 6320 l 10535 6341 l 10557 6363 l 10578 6385 l 10599 6407 l 10619 6430 l 10640 6453 l 10660 6477 l 10679 6500 l 10698 6523 l 10717 6546 l 10735 6569 l 10753 6591 l 10770 6613 l 10786 6635 l 10802 6656 l 10818 6677 l 10833 6697 l 10848 6718 l 10863 6738 l 10877 6757 l 10892 6777 l 10906 6797 l 10921 6818 l 10936 6838 l 10951 6859 l 10966 6881 l 10981 6903 l 10997 6925 l 11012 6948 l 11028 6971 l 11043 6994 l 11059 7018 l 11074 7042 l 11090 7065 l 11105 7089 l 11120 7113 l 11134 7137 l 11148 7161 l 11162 7185 l 11175 7208 l 11188 7231 l 11201 7255 l 11213 7278 l 11226 7301 l 11238 7325 l 11249 7347 l 11260 7370 l 11270 7393 l 11282 7418 l 11293 7442 l 11304 7468 l 11315 7495 l 11326 7522 l 11337 7550 l 11349 7579 l 11360 7609 l 11371 7640 l 11382 7671 l 11393 7703 l 11404 7735 l 11414 7768 l 11424 7801 l 11434 7834 l 11444 7867 l 11453 7900 l 11462 7933 l 11470 7966 l 11478 7999 l 11486 8032 l 11493 8064 l 11500 8097 l 11506 8130 l 11513 8163 l 11518 8194 l 11524 8225 l 11529 8257 l 11534 8290 l 11539 8324 l 11544 8358 l 11548 8393 l 11553 8428 l 11557 8464 l 11562 8501 l 11566 8538 l 11570 8575 l 11573 8612 l 11577 8649 l 11581 8686 l 11584 8723 l 11587 8759 l 11590 8794 l 11593 8829 l 11595 8863 l 11598 8895 l 11600 8927 l 11602 8958 l 11604 8987 l 11606 9015 l 11607 9042 l 11609 9067 l 11610 9092 l 11611 9115 l 11613 9138 l 11614 9173 l 11616 9205 l 11617 9236 l 11619 9266 l 11620 9293 l 11621 9319 l 11622 9343 l 11623 9366 l 11623 9387 l 11624 9405 l 11624 9422 l 11624 9438 l 11625 9451 l 11625 9463 l 11625 9474 l 11625 9484 l 11625 9492 l 11625 9500 l 11625 9503 l 11625 9506 l 11624 9510 l 11623 9513 l 11622 9516 l 11620 9519 l 11616 9521 l 11612 9524 l 11606 9527 l 11599 9530 l 11590 9533 l 11580 9535 l 11567 9538 l 11553 9541 l 11536 9543 l 11516 9546 l 11494 9548 l 11469 9551 l 11442 9553 l 11411 9555 l 11377 9557 l 11340 9559 l 11300 9562 l 11256 9563 l 11209 9565 l 11159 9567 l 11105 9569 l 11047 9571 l 10986 9572 l 10921 9574 l 10852 9575 l 10780 9577 l 10704 9578 l 10624 9579 l 10541 9581 l 10453 9582 l 10362 9583 l 10266 9584 l 10166 9585 l 10061 9586 l 9952 9587 l 9838 9588 l 9778 9588 l 9718 9588 l 9656 9589 l 9592 9589 l 9528 9589 l 9462 9590 l 9394 9590 l 9325 9590 l 9254 9591 l 9183 9591 l 9109 9591 l 9034 9592 l 8958 9592 l 8881 9592 l 8802 9593 l 8721 9593 l 8640 9593 l 8556 9594 l 8472 9594 l 8386 9594 l 8299 9594 l 8211 9595 l 8122 9595 l 8031 9595 l 7940 9595 l 7847 9596 l 7753 9596 l 7658 9596 l 7563 9596 l 7466 9596 l 7369 9597 l 7271 9597 l 7172 9597 l 7072 9597 l 6972 9597 l 6872 9597 l 6771 9598 l 6670 9598 l 6568 9598 l 6466 9598 l 6364 9598 l 6262 9598 l 6161 9598 l 6059 9599 l 5957 9599 l 5855 9599 l 5754 9599 l 5653 9599 l 5553 9599 l 5453 9599 l 5353 9599 l 5254 9599 l 5156 9599 l 5059 9599 l 4962 9599 l 4867 9599 l 4772 9600 l 4678 9600 l 4585 9600 l 4494 9600 l 4403 9600 l 4314 9600 l 4226 9600 l 4139 9600 l 4053 9600 l 3969 9600 l 3885 9600 l 3804 9600 l 3723 9600 l 3644 9600 l 3567 9600 l 3491 9600 l 3416 9600 l 3342 9600 l 3271 9600 l 3200 9600 l 3131 9600 l 3063 9600 l 2997 9600 l 2933 9600 l 2869 9600 l 2807 9600 l 2747 9600 l 2688 9600 l 2578 9600 l 2474 9600 l 2373 9600 l 2277 9600 l 2185 9600 l 2096 9600 l 2012 9599 l 1931 9599 l 1853 9599 l 1779 9598 l 1708 9597 l 1641 9597 l 1577 9596 l 1517 9595 l 1459 9594 l 1405 9592 l 1355 9590 l 1307 9589 l 1263 9587 l 1221 9584 l 1183 9582 l 1148 9579 l 1115 9576 l 1086 9573 l 1059 9570 l 1035 9566 l 1013 9562 l 994 9558 l 977 9553 l 963 9548 l 950 9543 l 939 9538 l 930 9532 l 922 9526 l 916 9520 l 911 9514 l 908 9507 l 905 9500 l 903 9492 l 901 9484 l 901 9476 l 900 9468 l 900 9459 l 900 9450 l 900 9434 l 900 9416 l 900 9397 l 900 9376 l 900 9355 l 900 9331 l 901 9307 l 901 9281 l 901 9254 l 902 9226 l 902 9197 l 903 9167 l 903 9136 l 904 9105 l 905 9074 l 906 9042 l 908 9011 l 909 8980 l 911 8949 l 912 8919 l 914 8889 l 916 8860 l 918 8832 l 920 8804 l 922 8777 l cp gs col7 0.75 shd ef gr % Polyline 15.000 slw n 347 8073 m 1398 6255 l 2437 6855 l 1387 8674 l 347 8073 l cp gs col0 s gr % Polyline n 5925 4875 m 8030 4875 l 8029 6072 l 5930 6074 l 5925 4875 l cp gs col0 s gr % Polyline n 8770 4916 m 10744 5636 l 10335 6761 l 8365 6047 l 8770 4916 l cp gs col0 s gr % Polyline n 11475 6525 m 12229 8490 l 11117 8920 l 10359 6959 l 11475 6525 l cp gs col0 s gr % Polyline n 3075 5025 m 5175 4877 l 5258 6072 l 3164 6221 l 3075 5025 l cp gs col0 s gr % Polyline n 450 9000 m 2400 5700 l 5700 5400 l 8475 5400 l 10875 6300 l 11925 9300 l gs col0 s gr $F2psEnd rs %%EndDocument endTexFig 1249 4289 a FD(Figure)f(2.)38 b FE(P)n(olyhedral)26 b(appro)n(ximation.)1340 2842 y Fi(b)1330 2861 y FC(U)1390 2830 y Fp(\016)2060 3168 y FC(~)-36 b(n)2108 3176 y Fp(i)2456 2842 y Fi(b)2440 2861 y FC(B)2502 2830 y Fp(j)2053 3433 y Fi(b)2038 3452 y FC(R)2097 3420 y Fp(i)1707 3853 y Fh(f)p FC(v)25 b FE(=)c Fh(\000)p FE(1)p Fh(g)218 4536 y FA(Using)40 b(Theorem)h(3.4,)k(w)m(e)d(can)f(reduce)g(the)g(pro)s(of) g(of)g(Prop)s(osition)e(3.2)j(to)g(the)f(computation)118 4644 y(of)35 b(the)h(probabilit)m(y)d(of)i Fu(fkM)1165 4658 y Fs(N)s(;K)1336 4644 y Fu(\000)24 b Fv(m)1511 4611 y Ft(\003)1550 4644 y FA(1)-25 b(I)1612 4660 y Fk(b)1603 4677 y Fs(V)1664 4644 y Fu(k)1709 4658 y Fx(1)1782 4644 y Fr(6)33 b Fv(\016)s Fu(g)p FA(.)57 b(According)34 b(to)i(\(3.3\))h (the)f(estimates)g(can)f(b)s(e)118 4751 y(restated)30 b(in)e(terms)h(of)g(the)g(mesoscopic)g(phase)g(lab)s(els.)38 b(It)30 b(will)c(b)s(e)i(enough)h(to)h(sho)m(w)f(that)g(:)40 b(for)29 b(an)m(y)118 4859 y Fv(\016)g(>)c FA(0,)31 b(there)g(exists)f Fv(\020)h FA(=)25 b Fv(\020)7 b FA(\()p Fv(\016)s FA(\))32 b(and)e Fv(K)1481 4873 y Fx(0)1520 4859 y FA(\()p Fv(\016)s FA(\))i(suc)m(h)e(that)h(for)f(all)f Fv(K)j Fr(>)25 b Fv(K)2614 4873 y Fx(0)544 5063 y FA(lim)15 b(inf)568 5124 y Fs(N)7 b Ft(!1)931 5002 y FA(1)p 846 5042 214 4 v 846 5125 a Fv(N)929 5099 y Fs(d)p Ft(\000)p Fx(1)1085 5063 y FA(log)17 b Fv(\026)1273 5025 y Fx(+)1273 5092 y Fs(\014)s(;N)1418 4962 y Fq(\020)1472 5063 y Fu(k)p Fv(u)1569 5019 y Fs(\020)1569 5092 y(N)s(;K)1737 5063 y Fu(\000)j FA(1)-25 b(I)1890 5080 y Fk(b)1881 5097 y Fs(V)1942 5063 y Fu(k)1987 5077 y Fx(1)2052 5063 y Fr(6)25 b Fv(\016)2191 4962 y Fq(\021)2286 5063 y Fr(>)46 b Fu(\000)20 b(W)2584 5078 y Fs(\014)2631 5063 y FA(\()2677 5040 y Fq(b)2666 5063 y Fv(V)g FA(\))h Fu(\000)f Fv(o)p FA(\()p Fv(\016)s FA(\))p Fv(;)407 b FA(\(3.5\))118 5262 y(where)30 b(the)h(function)e Fv(o)p FA(\()p Fv(\016)s FA(\))j(v)-5 b(anishes)29 b(as)h Fv(\016)k FA(go)s(es)d(to)g(0.)118 5478 y Fn(Step)i(2)g(:)42 b(L)-5 b(o)g(c)g(alization)36 b(of)d(the)g(interfac)-5 b(e.)p 118 5510 1480 4 v eop %%Page: 12 12 12 11 bop 118 45 a Fx(12)1460 b(T.)23 b(BODINEA)n(U)218 366 y FA(In)f(order)h(to)h(imp)s(ose)d(the)j(phase)e(segregation,)k(w)m (e)e(will)c(enforce)k(the)f(o)s(ccurrence)g(of)h(a)f(microscopic)118 481 y(in)m(terface)31 b(along)g(the)g(b)s(oundary)e Fv(@)1361 458 y Fq(b)1350 481 y Fv(V)20 b FA(.)42 b(The)30 b(images)h(of)2091 458 y Fq(b)2080 481 y Fv(V)20 b FA(,)2226 458 y Fq(b)2209 481 y Fv(R)2279 448 y Fs(i)2338 481 y FA(and)2528 458 y Fq(b)2515 481 y Fv(U)2587 448 y Fs(\016)2656 481 y FA(in)29 b Fy(D)2822 495 y Fs(N)2925 481 y FA(will)g(b)s(e)h(denoted)g (b)m(y)118 595 y Fv(V)171 609 y Fs(N)238 595 y FA(,)g Fv(R)363 562 y Fs(i)362 622 y(N)458 595 y FA(and)e Fv(U)705 562 y Fs(\016)695 622 y(N)763 595 y FA(.)40 b(W)-8 b(e)30 b(split)d Fv(R)1254 562 y Fs(i)1253 622 y(N)1349 595 y FA(in)m(to)i Fv(R)1602 551 y Fs(i;)p Ft(\000)1601 624 y Fs(N)1733 595 y FA(and)f Fv(R)1978 551 y Fs(i;)p Fx(+)1977 624 y Fs(N)2110 595 y FA(whic)m(h)f(are)j(the)f(microscopic)f(coun)m (terparts)118 721 y(of)233 698 y Fq(b)222 721 y Fv(V)40 b Fu(\\)413 698 y Fq(b)396 721 y Fv(R)466 688 y Fs(i)524 721 y FA(and)718 698 y Fq(b)701 721 y Fv(R)771 688 y Fs(i)819 721 y Fu(n)896 698 y Fq(b)885 721 y Fv(V)20 b FA(.)954 865 y 15010666 9323399 0 0 39863746 24733941 startTexFig 954 865 a %%BeginDocument: ./pictures/lower2.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: lower2.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Mon Sep 11 14:02:19 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 606 376 %%Magnification: 0.9900 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 376 moveto 0 0 lineto 606 0 lineto 606 376 lineto closepath clip newpath % Fill background color 0 0 moveto 606 0 lineto 606 376 lineto 0 376 lineto closepath 1.00 1.00 1.00 setrgbcolor fill 7.0 372.0 translate 1 -1 scale .9 .9 scale % to make patterns same scale as in xfig % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index show % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proe char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % right45 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 32 true [ 32 0 0 -32 0 32 ] {<010101010202020204040404080808081010101020202020 404040408080808001010101020202020404040408080808 101010102020202040404040808080800101010102020202 040404040808080810101010202020204040404080808080 010101010202020204040404080808081010101020202020 4040404080808080>} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P5 exch def 1.1111 1.1111 scale %restore scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /hypen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.05940 0.05940 sc % Polyline 7.500 slw gs clippath 621 3353 m 529 3316 l 444 3529 l 564 3364 l 536 3566 l cp eoclip n 75 4589 m 570 3349 l gs col0 s gr gr % arrowhead n 536 3566 m 564 3364 l 444 3529 l 536 3566 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 1801 2161 m 1845 2072 l 1640 1970 l 1796 2103 l 1596 2058 l cp eoclip n 818 1615 m 1810 2110 l gs col0 s gr gr % arrowhead n 1596 2058 m 1796 2103 l 1640 1970 l 1596 2058 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 3577 5248 m 3540 5156 l 3327 5241 l 3530 5214 l 3364 5333 l cp eoclip n 3545 5208 m 1686 5951 l gs col0 s gr gr % arrowhead n 3364 5333 m 3530 5214 l 3327 5241 l 3364 5333 l cp gs 0.00 setgray ef gr col0 s % Polyline n 2182 1118 m 7634 1118 l 7634 5084 l 2182 5084 l cp gs col0 s gr % Polyline [15 45] 45 sd n 2182 2110 m 7634 2110 l 7634 4092 l 2182 4092 l cp gs col0 s gr [] 0 sd % Polyline n 739 3135 m 9166 3135 l gs col0 s gr % Polyline n 2189 1136 m 7623 1136 l 7623 2112 l 2189 2112 l cp gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 145.93 75.73] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline n 2189 5084 m 7637 5084 l 7637 4093 l 2189 4093 l cp gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P5 [16 0 0 -16 145.93 272.87] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline gs clippath 9930 2385 m 9870 2385 l 9870 2570 l 9900 2420 l 9930 2570 l cp eoclip n 9900 3300 m 9900 2400 l gs col0 s gr gr % arrowhead n 9930 2570 m 9900 2420 l 9870 2570 l 9900 2540 l 9930 2570 l cp gs 0.00 setgray ef gr col0 s % Polyline 45.000 slw n 2206 1490 m 2207 1490 l 2211 1488 l 2221 1485 l 2238 1479 l 2261 1471 l 2289 1462 l 2320 1452 l 2350 1442 l 2379 1432 l 2405 1424 l 2429 1417 l 2450 1412 l 2468 1407 l 2484 1404 l 2499 1401 l 2512 1399 l 2526 1398 l 2539 1398 l 2552 1398 l 2564 1400 l 2575 1402 l 2586 1406 l 2596 1410 l 2604 1415 l 2612 1420 l 2620 1426 l 2626 1432 l 2631 1439 l 2636 1446 l 2640 1453 l 2646 1464 l 2650 1475 l 2655 1488 l 2658 1502 l 2660 1516 l 2662 1531 l 2662 1545 l 2661 1559 l 2660 1572 l 2657 1585 l 2653 1597 l 2648 1610 l 2642 1623 l 2635 1637 l 2629 1651 l 2622 1665 l 2616 1679 l 2610 1692 l 2606 1705 l 2603 1717 l 2602 1726 l 2601 1736 l 2602 1745 l 2603 1755 l 2604 1766 l 2607 1777 l 2611 1788 l 2616 1799 l 2621 1810 l 2628 1821 l 2635 1832 l 2643 1842 l 2651 1852 l 2660 1862 l 2671 1872 l 2682 1882 l 2694 1892 l 2708 1902 l 2723 1912 l 2738 1922 l 2755 1932 l 2772 1941 l 2789 1950 l 2806 1957 l 2823 1964 l 2839 1969 l 2855 1974 l 2871 1978 l 2889 1981 l 2907 1983 l 2926 1984 l 2944 1984 l 2963 1983 l 2981 1980 l 2999 1977 l 3015 1973 l 3030 1969 l 3043 1964 l 3055 1958 l 3065 1953 l 3074 1947 l 3082 1941 l 3089 1934 l 3095 1926 l 3100 1918 l 3105 1910 l 3108 1901 l 3110 1892 l 3112 1883 l 3112 1875 l 3112 1866 l 3111 1858 l 3110 1847 l 3108 1837 l 3105 1825 l 3101 1813 l 3097 1801 l 3092 1788 l 3086 1777 l 3081 1766 l 3075 1756 l 3070 1746 l 3064 1737 l 3058 1728 l 3051 1719 l 3044 1710 l 3038 1700 l 3031 1690 l 3025 1680 l 3020 1671 l 3015 1661 l 3012 1651 l 3008 1640 l 3006 1629 l 3004 1616 l 3003 1603 l 3004 1589 l 3005 1575 l 3007 1562 l 3010 1549 l 3015 1538 l 3020 1527 l 3026 1517 l 3034 1508 l 3043 1499 l 3053 1490 l 3064 1483 l 3076 1476 l 3089 1470 l 3101 1466 l 3112 1463 l 3124 1462 l 3133 1461 l 3143 1461 l 3153 1462 l 3164 1464 l 3174 1467 l 3185 1471 l 3195 1476 l 3205 1482 l 3215 1488 l 3224 1495 l 3232 1503 l 3240 1511 l 3247 1520 l 3254 1529 l 3262 1540 l 3269 1552 l 3277 1565 l 3284 1579 l 3292 1593 l 3299 1607 l 3306 1621 l 3313 1634 l 3319 1647 l 3326 1659 l 3333 1671 l 3340 1684 l 3347 1697 l 3355 1710 l 3363 1723 l 3371 1736 l 3379 1749 l 3387 1762 l 3395 1773 l 3402 1784 l 3409 1795 l 3416 1804 l 3424 1816 l 3432 1827 l 3441 1838 l 3450 1849 l 3460 1860 l 3470 1870 l 3481 1880 l 3492 1888 l 3503 1896 l 3516 1903 l 3526 1909 l 3538 1914 l 3552 1919 l 3566 1923 l 3582 1926 l 3599 1929 l 3616 1931 l 3634 1931 l 3652 1930 l 3670 1928 l 3688 1925 l 3706 1920 l 3719 1915 l 3733 1909 l 3748 1903 l 3763 1895 l 3779 1887 l 3796 1878 l 3813 1868 l 3830 1857 l 3847 1846 l 3864 1834 l 3881 1823 l 3898 1811 l 3913 1800 l 3929 1789 l 3943 1778 l 3958 1767 l 3972 1756 l 3986 1746 l 4000 1735 l 4015 1724 l 4030 1712 l 4045 1701 l 4061 1689 l 4076 1677 l 4091 1666 l 4106 1654 l 4120 1643 l 4134 1632 l 4147 1622 l 4160 1612 l 4173 1603 l 4185 1593 l 4199 1583 l 4213 1572 l 4227 1562 l 4242 1552 l 4257 1542 l 4273 1533 l 4289 1524 l 4305 1517 l 4321 1511 l 4337 1506 l 4352 1503 l 4367 1501 l 4382 1501 l 4396 1503 l 4409 1505 l 4422 1509 l 4436 1515 l 4450 1521 l 4465 1529 l 4480 1538 l 4495 1548 l 4510 1558 l 4524 1569 l 4539 1581 l 4553 1592 l 4566 1604 l 4578 1615 l 4590 1626 l 4601 1637 l 4611 1647 l 4624 1660 l 4636 1672 l 4648 1685 l 4660 1697 l 4672 1710 l 4684 1722 l 4695 1733 l 4707 1744 l 4718 1754 l 4729 1763 l 4740 1771 l 4751 1779 l 4763 1786 l 4775 1794 l 4789 1801 l 4803 1808 l 4818 1814 l 4833 1821 l 4848 1826 l 4863 1831 l 4877 1835 l 4889 1838 l 4901 1840 l 4912 1841 l 4921 1842 l 4929 1842 l 4937 1841 l 4945 1840 l 4952 1838 l 4960 1835 l 4967 1832 l 4973 1828 l 4979 1823 l 4985 1818 l 4990 1812 l 4994 1806 l 4999 1799 l 5003 1792 l 5008 1783 l 5012 1773 l 5017 1762 l 5021 1750 l 5025 1738 l 5028 1724 l 5031 1711 l 5033 1697 l 5034 1684 l 5034 1671 l 5033 1659 l 5032 1647 l 5030 1636 l 5026 1625 l 5022 1613 l 5017 1602 l 5011 1590 l 5005 1578 l 4998 1566 l 4991 1554 l 4984 1543 l 4978 1532 l 4971 1521 l 4966 1511 l 4959 1498 l 4953 1485 l 4947 1471 l 4942 1457 l 4938 1443 l 4936 1429 l 4935 1417 l 4935 1405 l 4937 1395 l 4941 1387 l 4944 1382 l 4948 1378 l 4953 1374 l 4959 1370 l 4965 1368 l 4973 1366 l 4981 1365 l 4990 1364 l 5000 1365 l 5010 1367 l 5020 1370 l 5031 1373 l 5043 1378 l 5054 1384 l 5066 1391 l 5078 1399 l 5088 1407 l 5100 1416 l 5112 1426 l 5124 1437 l 5138 1449 l 5151 1462 l 5166 1476 l 5181 1490 l 5196 1505 l 5211 1520 l 5227 1535 l 5242 1549 l 5257 1564 l 5272 1578 l 5287 1591 l 5301 1603 l 5315 1615 l 5329 1626 l 5345 1638 l 5361 1649 l 5377 1660 l 5394 1670 l 5411 1680 l 5429 1689 l 5447 1699 l 5465 1707 l 5483 1715 l 5501 1723 l 5518 1730 l 5535 1737 l 5552 1743 l 5567 1748 l 5583 1754 l 5598 1759 l 5613 1764 l 5628 1769 l 5643 1773 l 5659 1778 l 5675 1783 l 5691 1788 l 5708 1793 l 5725 1798 l 5741 1803 l 5758 1807 l 5774 1812 l 5789 1816 l 5804 1819 l 5818 1823 l 5832 1826 l 5846 1829 l 5861 1832 l 5877 1835 l 5893 1838 l 5909 1840 l 5926 1843 l 5943 1845 l 5960 1847 l 5977 1848 l 5994 1849 l 6010 1850 l 6025 1851 l 6040 1851 l 6054 1850 l 6068 1850 l 6082 1849 l 6096 1847 l 6110 1845 l 6125 1843 l 6140 1840 l 6155 1837 l 6170 1832 l 6185 1828 l 6199 1822 l 6213 1816 l 6226 1810 l 6239 1803 l 6251 1796 l 6263 1788 l 6274 1780 l 6285 1770 l 6297 1760 l 6309 1750 l 6321 1738 l 6334 1726 l 6347 1713 l 6360 1701 l 6373 1689 l 6386 1677 l 6400 1665 l 6413 1655 l 6426 1645 l 6440 1635 l 6452 1628 l 6465 1620 l 6479 1613 l 6494 1606 l 6510 1599 l 6527 1593 l 6545 1587 l 6564 1580 l 6583 1575 l 6603 1569 l 6624 1564 l 6644 1559 l 6665 1555 l 6686 1551 l 6707 1547 l 6729 1544 l 6747 1541 l 6766 1538 l 6785 1535 l 6805 1532 l 6826 1530 l 6847 1527 l 6869 1524 l 6892 1522 l 6914 1520 l 6937 1517 l 6960 1515 l 6982 1513 l 7004 1512 l 7025 1510 l 7045 1509 l 7064 1508 l 7082 1507 l 7099 1507 l 7115 1506 l 7130 1506 l 7154 1507 l 7176 1508 l 7197 1509 l 7216 1512 l 7235 1515 l 7252 1518 l 7267 1523 l 7281 1528 l 7292 1533 l 7303 1539 l 7312 1545 l 7320 1552 l 7328 1560 l 7337 1569 l 7345 1580 l 7353 1591 l 7360 1604 l 7368 1617 l 7376 1631 l 7383 1644 l 7391 1658 l 7398 1671 l 7405 1683 l 7413 1695 l 7421 1708 l 7430 1721 l 7440 1735 l 7450 1748 l 7461 1762 l 7472 1775 l 7483 1786 l 7493 1797 l 7504 1807 l 7514 1816 l 7527 1826 l 7540 1835 l 7554 1843 l 7567 1851 l 7581 1858 l 7594 1864 l 7605 1869 l 7615 1873 l 7624 1876 l 7630 1879 l 7632 1879 l 7633 1880 l 7634 1880 l 7635 1881 l 7636 1881 l 7637 1882 l 7638 1882 l 7639 1883 l 7640 1883 l 7640 1884 l 7641 1885 l 7640 1885 l 7640 1886 l 7639 1886 l 7638 1886 l 7637 1887 l 7636 1887 l 7635 1887 l 7634 1887 l gs col0 s gr % Polyline n 2182 4761 m 2184 4758 l 2187 4752 l 2194 4742 l 2203 4726 l 2216 4705 l 2232 4680 l 2249 4652 l 2268 4621 l 2287 4591 l 2306 4560 l 2324 4531 l 2341 4504 l 2357 4479 l 2372 4456 l 2385 4436 l 2398 4418 l 2409 4402 l 2419 4387 l 2429 4374 l 2438 4363 l 2446 4353 l 2456 4341 l 2466 4331 l 2475 4323 l 2484 4315 l 2493 4308 l 2501 4303 l 2510 4299 l 2518 4295 l 2527 4293 l 2535 4292 l 2543 4292 l 2551 4293 l 2558 4295 l 2566 4297 l 2573 4300 l 2581 4303 l 2588 4307 l 2595 4312 l 2605 4317 l 2616 4324 l 2627 4332 l 2639 4340 l 2651 4349 l 2663 4359 l 2675 4370 l 2686 4381 l 2697 4392 l 2707 4404 l 2716 4416 l 2724 4428 l 2730 4440 l 2736 4452 l 2740 4464 l 2743 4477 l 2746 4491 l 2747 4505 l 2748 4521 l 2748 4537 l 2747 4553 l 2746 4570 l 2745 4587 l 2743 4604 l 2741 4620 l 2739 4636 l 2737 4651 l 2735 4667 l 2734 4682 l 2733 4698 l 2732 4715 l 2732 4731 l 2732 4749 l 2733 4766 l 2735 4784 l 2738 4801 l 2742 4817 l 2747 4833 l 2753 4847 l 2759 4861 l 2767 4874 l 2777 4885 l 2784 4894 l 2793 4902 l 2803 4910 l 2814 4918 l 2826 4925 l 2839 4932 l 2853 4938 l 2868 4944 l 2884 4949 l 2900 4954 l 2916 4957 l 2933 4960 l 2950 4962 l 2967 4963 l 2983 4963 l 3000 4963 l 3016 4962 l 3033 4960 l 3051 4956 l 3070 4952 l 3090 4946 l 3110 4940 l 3130 4933 l 3151 4925 l 3172 4916 l 3193 4907 l 3214 4898 l 3234 4888 l 3253 4879 l 3271 4870 l 3287 4862 l 3303 4854 l 3317 4847 l 3330 4840 l 3344 4833 l 3358 4827 l 3371 4821 l 3384 4815 l 3397 4810 l 3410 4805 l 3423 4800 l 3437 4795 l 3451 4790 l 3465 4784 l 3480 4779 l 3495 4774 l 3511 4768 l 3528 4762 l 3543 4757 l 3558 4751 l 3575 4745 l 3592 4738 l 3611 4731 l 3632 4723 l 3653 4715 l 3674 4707 l 3696 4699 l 3719 4690 l 3741 4682 l 3763 4674 l 3784 4665 l 3805 4658 l 3825 4650 l 3844 4643 l 3862 4636 l 3880 4630 l 3898 4623 l 3917 4616 l 3935 4610 l 3953 4604 l 3970 4599 l 3988 4594 l 4005 4591 l 4022 4588 l 4038 4586 l 4053 4586 l 4068 4587 l 4082 4589 l 4095 4592 l 4108 4596 l 4120 4602 l 4131 4609 l 4142 4618 l 4154 4628 l 4165 4639 l 4177 4652 l 4189 4666 l 4202 4681 l 4215 4697 l 4228 4713 l 4241 4730 l 4254 4746 l 4268 4761 l 4281 4776 l 4294 4790 l 4307 4802 l 4320 4813 l 4334 4823 l 4347 4832 l 4362 4839 l 4376 4846 l 4392 4851 l 4408 4855 l 4425 4858 l 4441 4859 l 4458 4859 l 4474 4858 l 4490 4856 l 4505 4853 l 4519 4849 l 4532 4844 l 4544 4838 l 4555 4831 l 4565 4824 l 4575 4814 l 4584 4804 l 4592 4791 l 4599 4778 l 4605 4763 l 4610 4746 l 4614 4728 l 4618 4710 l 4620 4690 l 4621 4670 l 4622 4650 l 4621 4630 l 4620 4609 l 4619 4588 l 4617 4569 l 4615 4550 l 4613 4530 l 4611 4508 l 4608 4486 l 4605 4464 l 4602 4441 l 4600 4419 l 4597 4396 l 4595 4374 l 4593 4354 l 4591 4334 l 4590 4316 l 4589 4299 l 4589 4284 l 4589 4270 l 4590 4259 l 4591 4250 l 4593 4240 l 4595 4232 l 4597 4224 l 4600 4216 l 4604 4209 l 4607 4203 l 4612 4197 l 4616 4193 l 4621 4189 l 4627 4186 l 4632 4183 l 4638 4182 l 4644 4181 l 4650 4181 l 4657 4182 l 4663 4183 l 4670 4185 l 4676 4187 l 4685 4191 l 4694 4196 l 4704 4203 l 4714 4210 l 4725 4219 l 4736 4229 l 4747 4241 l 4758 4254 l 4770 4267 l 4781 4282 l 4792 4298 l 4802 4314 l 4812 4331 l 4821 4349 l 4829 4367 l 4838 4386 l 4844 4403 l 4851 4421 l 4857 4441 l 4864 4461 l 4870 4482 l 4877 4505 l 4883 4527 l 4890 4551 l 4896 4574 l 4903 4598 l 4909 4621 l 4916 4643 l 4923 4665 l 4929 4686 l 4936 4705 l 4943 4724 l 4950 4741 l 4958 4757 l 4965 4773 l 4974 4787 l 4982 4801 l 4992 4815 l 5002 4828 l 5013 4840 l 5024 4851 l 5036 4862 l 5049 4872 l 5061 4881 l 5074 4888 l 5087 4895 l 5100 4901 l 5113 4905 l 5126 4909 l 5138 4912 l 5151 4913 l 5164 4915 l 5178 4915 l 5193 4914 l 5208 4912 l 5224 4910 l 5240 4906 l 5257 4901 l 5274 4895 l 5292 4889 l 5309 4881 l 5326 4873 l 5343 4865 l 5360 4855 l 5375 4846 l 5391 4836 l 5405 4826 l 5420 4816 l 5434 4805 l 5448 4793 l 5462 4781 l 5477 4768 l 5492 4755 l 5507 4741 l 5523 4727 l 5538 4713 l 5554 4699 l 5569 4685 l 5584 4671 l 5598 4658 l 5612 4646 l 5625 4635 l 5638 4624 l 5651 4614 l 5664 4604 l 5677 4595 l 5690 4586 l 5704 4578 l 5718 4570 l 5732 4563 l 5747 4557 l 5762 4552 l 5777 4548 l 5791 4546 l 5805 4545 l 5819 4545 l 5832 4547 l 5845 4549 l 5858 4554 l 5870 4559 l 5882 4566 l 5894 4575 l 5907 4585 l 5920 4596 l 5934 4608 l 5949 4621 l 5965 4634 l 5982 4648 l 5999 4661 l 6017 4674 l 6036 4686 l 6055 4697 l 6075 4706 l 6095 4714 l 6116 4720 l 6138 4724 l 6157 4727 l 6176 4728 l 6197 4728 l 6219 4727 l 6242 4725 l 6265 4722 l 6290 4718 l 6315 4713 l 6341 4707 l 6366 4700 l 6391 4693 l 6416 4685 l 6440 4676 l 6464 4668 l 6486 4659 l 6507 4649 l 6526 4640 l 6544 4631 l 6561 4622 l 6576 4613 l 6596 4600 l 6614 4587 l 6630 4573 l 6645 4560 l 6659 4546 l 6671 4533 l 6682 4520 l 6691 4508 l 6700 4497 l 6708 4487 l 6714 4478 l 6721 4471 l 6727 4465 l 6734 4460 l 6740 4457 l 6748 4455 l 6756 4454 l 6765 4454 l 6775 4456 l 6785 4460 l 6797 4465 l 6809 4472 l 6821 4480 l 6834 4489 l 6847 4500 l 6860 4512 l 6873 4525 l 6887 4539 l 6897 4550 l 6909 4563 l 6921 4577 l 6933 4591 l 6946 4606 l 6960 4622 l 6975 4639 l 6989 4656 l 7004 4673 l 7019 4689 l 7035 4706 l 7050 4722 l 7065 4736 l 7079 4750 l 7093 4763 l 7107 4775 l 7121 4785 l 7134 4795 l 7147 4803 l 7161 4810 l 7174 4817 l 7188 4822 l 7202 4826 l 7216 4829 l 7230 4831 l 7245 4832 l 7259 4831 l 7273 4830 l 7287 4827 l 7300 4823 l 7313 4818 l 7326 4812 l 7337 4804 l 7349 4797 l 7359 4788 l 7370 4778 l 7381 4766 l 7392 4753 l 7403 4738 l 7414 4722 l 7425 4705 l 7436 4688 l 7447 4669 l 7458 4650 l 7468 4631 l 7478 4612 l 7488 4595 l 7497 4578 l 7506 4562 l 7515 4547 l 7523 4534 l 7531 4522 l 7543 4505 l 7556 4491 l 7568 4478 l 7581 4468 l 7593 4460 l 7604 4454 l 7614 4449 l 7622 4446 l 7629 4444 l 7634 4443 l 7635 4443 l 7636 4443 l 7637 4442 l 7638 4442 l 7639 4442 l 7640 4442 l 7640 4441 l 7641 4441 l 7642 4441 l 7642 4440 l 7641 4440 l 7640 4440 l 7639 4439 l 7638 4439 l 7637 4439 l 7636 4439 l 7635 4439 l 7634 4439 l gs col0 s gr /Times-Roman-iso ff 285.00 scf sf 3545 1738 m gs 1 -1 sc (+) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 2801 1738 m gs 1 -1 sc (+) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 5403 1615 m gs 1 -1 sc (+ +) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 6643 1490 m gs 1 -1 sc (+ +) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 3669 4960 m gs 1 -1 sc (_ _) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 5651 4836 m gs 1 -1 sc (_ _) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 7881 3101 m gs 1 -1 sc 90.0 rot ( + + + +) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 2182 3101 m gs 1 -1 sc 90.0 rot ( + + + +) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 942 3349 m gs 1 -1 sc (- - -) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 7758 3473 m gs 1 -1 sc 270.0 rot (- - -) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 8006 3349 m gs 1 -1 sc (- - -) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 1934 3473 m gs 1 -1 sc 270.0 rot (- - -) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 694 3056 m gs 1 -1 sc ( + + + +) col0 sh gr /Times-Roman-iso ff 285.00 scf sf 7679 3056 m gs 1 -1 sc ( + + + +) col0 sh gr % Polyline 7.500 slw gs clippath 5990 1358 m 6037 1396 l 6131 1278 l 6033 1353 l 6084 1240 l cp eoclip n 7014 127 m 6023 1366 l gs col0 s gr gr % arrowhead n 6084 1240 m 6033 1353 l 6131 1278 l 6084 1240 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 6658 4806 m 6609 4840 l 6696 4964 l 6652 4849 l 6745 4930 l cp eoclip n 6643 4836 m 7510 6075 l gs col0 s gr gr % arrowhead n 6745 4930 m 6652 4849 l 6696 4964 l 6745 4930 l cp gs 0.00 setgray ef gr col0 s $F2psEnd rs end %%EndDocument endTexFig 979 2301 a FD(Figure)28 b(3.)38 b FE(Microscopic)28 b(in)n(terface)f(lo)r(calized)g(close)g(to)f FC(B)2753 2270 y Fp(i)2779 2301 y FE(.)786 1819 y FC(U)846 1787 y Fp(\016)838 1834 y(N)999 1181 y Fh(B)1051 1149 y Fp(i;)p Fm(+)2345 921 y Fg(R)2408 886 y Fp(i;)p Fm(+)2408 942 y Fp(N)2345 2055 y Fh(A)2406 2023 y Fp(i;)p Fl(\000)1093 2055 y Fg(R)1156 2019 y Fp(i;)p Fl(\000)1156 2076 y Fp(N)2863 1464 y FC(~)-36 b(n)2911 1472 y Fp(i)218 2498 y FA(First,)39 b(w)m(e)f(imp)s(ose)f(the)h(microscopic)f(constrain)m(t)h(that)g(there) h(is)d(a)j(+)e(surface)h(of)g(spins)e(in)g(the)118 2613 y(upp)s(er)c(half)h(of)g Fv(R)741 2569 y Fs(i;)p Fx(+)740 2641 y Fs(N)878 2613 y FA(\(see)h(\014gure)f(3\).)52 b(Let)1660 2590 y Fq(b)1642 2613 y Fv(Q)1714 2580 y Fs(i)1776 2613 y FA(b)s(e)33 b(the)h(parallelepip)s(ed)c(included)h(in)3144 2590 y Fq(b)3126 2613 y Fv(R)3196 2580 y Fs(i)3258 2613 y FA(with)h(basis)137 2715 y Fq(b)118 2738 y Fv(B)192 2705 y Fs(i)253 2738 y FA(and)h(heigh)m(t)721 2703 y Fs(\016)r(h)p 721 2718 75 4 v 740 2770 a Fx(2)805 2738 y FA(.)49 b(W)-8 b(e)35 b(de\014ne)d(the)i(microscopic)e(region)h Fj(R)2308 2694 y Fs(i;)p Fx(+)2308 2767 y Fs(N)2444 2738 y FA(as)h Fv(R)2629 2694 y Fs(i;)p Fx(+)2628 2767 y Fs(N)2753 2738 y Fu(n)23 b Fv(Q)2893 2705 y Fs(i)2893 2765 y(N)2960 2738 y FA(.)49 b(Let)34 b Fu(A)3273 2705 y Fs(i;)p Fx(+)3409 2738 y FA(b)s(e)e(the)118 2866 y(ev)m(en)m(t)h(that)g(there)f(is)f(a)h (surface)g(of)f(spins)f(equal)i(to)g(1)g(crossing)f Fj(R)2456 2822 y Fs(i;)p Fx(+)2456 2895 y Fs(N)2591 2866 y FA(in)f(the)i (direction)f(orthogonal)118 2991 y(to)d Fv(~)-42 b(n)284 3005 y Fs(i)311 2991 y FA(.)41 b(In)29 b(the)h(same)g(w)m(a)m(y)-8 b(,)31 b(w)m(e)g(in)m(tro)s(duce)d(the)i(set)h Fj(R)1984 2947 y Fs(i;)p Ft(\000)1984 3020 y Fs(N)2116 2991 y FA(and)e(the)h(ev)m (en)m(t)i Fu(A)2761 2958 y Fs(i;)p Ft(\000)2892 2991 y FA(suc)m(h)e(that)g(there)g(is)f(a)118 3116 y(crossing)h(surface)g (of)h(spins)d(equal)i(to)h Fu(\000)p FA(1.)41 b(W)-8 b(e)31 b(set)g Fu(A)25 b FA(=)2126 3048 y Fq(T)2202 3074 y Fs(`)2202 3143 y(i)p Fx(=1)2335 3116 y Fu(A)2408 3083 y Fs(i;)p Fx(+)2531 3116 y Fu(\\)20 b(A)2685 3083 y Fs(i;)p Ft(\000)2787 3116 y FA(.)218 3228 y(Finally)-8 b(,)27 b(w)m(e)j(de\014ne)e Fu(B)1000 3195 y Fs(i;)p Fx(+)1131 3228 y FA(\(resp)g Fu(B)1420 3195 y Fs(i;)p Ft(\000)1522 3228 y FA(\))h(the)g(set)h(of)f(spin)d(con\014gurations)i(suc)m(h)h (that)g(the)g(spins)e(are)118 3347 y(equal)k(to)h(1)g(\(resp)f Fu(\000)p FA(1\))g(on)g(the)h(sides)e(of)i Fv(R)1638 3303 y Fs(i;)p Fx(+)1637 3376 y Fs(N)1771 3347 y FA(\(resp)f Fv(R)2070 3303 y Fs(i;)p Ft(\000)2069 3376 y Fs(N)2172 3347 y FA(\))h(parallel)d(to)h Fv(~)-43 b(n)2730 3361 y Fs(i)2758 3347 y FA(.)44 b(In)30 b(order)h(to)h(construct)118 3461 y(a)e(closed)g(con)m(tour)h(of)f(spins)e(surrounding)f Fv(V)1682 3475 y Fs(N)1749 3461 y FA(,)j(w)m(e)h(de\014ne)e Fu(B)j FA(as)f(the)f(set)g(of)g(con\014gurations)g(in)e Fu(B)3559 3428 y Fs(i;)p Fx(+)118 3569 y FA(and)d Fu(B)353 3536 y Fs(i;)p Ft(\000)480 3569 y FA(suc)m(h)g(that)h(the)f(spins)e(on) i(one)h(side)e(of)h Fv(U)1876 3536 y Fs(\016)1866 3596 y(N)1959 3569 y FA(are)g Fu(\000)g FA(and)g(+)g(in)f(the)h(other)g (side)g(\(see)h(\014gure)e(3\).)218 3785 y(An)m(y)34 b(spin)f(con\014guration)h(in)f Fu(A)23 b(\\)f(B)37 b FA(con)m(tains)e(a)g(microscopic)f(in)m(terface)h(whic)m(h)e(decouples) h Fv(V)3594 3799 y Fs(N)118 3893 y FA(from)c(its)g(complemen)m(t.)41 b(One)30 b(has)461 4078 y Fv(\026)516 4040 y Fx(+)516 4107 y Fs(\014)s(;N)661 3977 y Fq(\020)715 4078 y Fu(k)p Fv(u)812 4034 y Fs(\020)812 4107 y(N)s(;K)980 4078 y Fu(\000)20 b FA(1)-25 b(I)1133 4095 y Fk(b)1124 4112 y Fs(V)1185 4078 y Fu(k)1230 4092 y Fx(1)1295 4078 y Fr(6)25 b Fv(\016)1434 3977 y Fq(\021)1530 4078 y Fr(>)g Fv(\026)1681 4040 y Fx(+)1681 4107 y Fs(\014)s(;N)1825 3977 y Fq(\020)q(n)1940 4078 y Fu(k)p Fv(u)2037 4034 y Fs(\020)2037 4107 y(N)s(;K)2205 4078 y Fu(\000)20 b FA(1)-25 b(I)2358 4095 y Fk(b)2349 4112 y Fs(V)2410 4078 y Fu(k)2455 4092 y Fx(1)2520 4078 y Fr(6)25 b Fv(\016)2659 3977 y Fq(o)2741 4078 y Fu(\\)20 b(A)g(\\)f(B)3058 3977 y Fq(\021)3127 4078 y Fv(:)323 b FA(\(3.6\))118 4268 y(The)42 b(spin)e(con\014gurations)i(inside)e Fv(V)1443 4282 y Fs(N)1553 4268 y FA(\(resp)i Fv(V)1866 4235 y Fs(c)1846 4295 y(N)1913 4268 y FA(\))h(are)g(surrounded)d(b)m(y)i Fu(\000)g FA(\(resp)g(+\))g(b)s(oundary)118 4376 y(conditions,)29 b(so)i(that)g(they)g(are)g(in)e(equilibrium)c(in)k(the)i Fu(\000)f FA(\(resp)g(+\))h(pure)e(phase.)41 b(A)30 b(pro)s(of)g (similar)118 4484 y(to)39 b(the)e(one)i(of)e(Theorem)h(3.2)h(implies)c (that)j(one)g(can)g(c)m(ho)s(ose)h Fv(h)f FA(small)e(enough,)j Fv(\020)3124 4451 y Ft(0)3185 4484 y FA(=)e Fv(\020)3340 4451 y Ft(0)3363 4484 y FA(\()p Fv(\016)s FA(\))i(and)118 4592 y Fv(K)202 4559 y Ft(0)195 4616 y Fx(0)260 4592 y FA(=)25 b Fv(K)440 4559 y Ft(0)433 4616 y Fx(0)473 4592 y FA(\()p Fv(\016)s FA(\))31 b(suc)m(h)g(that)226 4811 y(lim)187 4872 y Fs(N)7 b Ft(!1)447 4811 y Fv(\026)502 4773 y Fx(+)502 4841 y Fs(\014)s(;N)647 4683 y Fq(\022)714 4688 y(Z)773 4877 y Fk(b)764 4894 y Fs(V)821 4875 y Fp(c)872 4811 y Fu(j)p Fv(u)949 4767 y Fs(\020)985 4744 y Fl(0)949 4840 y Fs(N)s(;K)1097 4811 y FA(\()p Fv(x)p FA(\))20 b Fu(\000)g FA(1)p Fu(j)15 b Fv(dx)27 b Fr(>)1647 4750 y Fv(\016)p 1647 4790 46 4 v 1647 4874 a FA(2)1732 4811 y(or)1859 4688 y Fq(Z)1918 4877 y Fk(b)1909 4894 y Fs(V)1985 4811 y Fu(j)p Fv(u)2062 4767 y Fs(\020)2098 4744 y Fl(0)2062 4840 y Fs(N)s(;K)2210 4811 y FA(\()p Fv(x)p FA(\))21 b(+)f(1)p Fu(j)15 b Fv(dx)26 b Fr(>)2761 4750 y Fv(\016)p 2760 4790 V 2760 4874 a FA(2)2846 4707 y Fq(\014)2846 4761 y(\014)2846 4816 y(\014)2906 4811 y Fu(A)20 b(\\)g(B)3143 4683 y Fq(\023)3235 4811 y FA(=)k(0)i Fv(;)218 5029 y FA(So)k(that)h(\(3.6\))h(can)f(b)s(e)f(rewritten)f(for)h Fv(N)40 b FA(large)31 b(enough)f(as)918 5235 y Fv(\026)973 5196 y Fx(+)973 5264 y Fs(\014)s(;N)1118 5134 y Fq(\020)1172 5235 y Fu(k)p Fv(u)1269 5190 y Fs(\020)1305 5167 y Fl(0)1269 5263 y Fs(N)s(;K)1437 5235 y Fu(\000)20 b FA(1)-25 b(I)1590 5251 y Fk(b)1581 5268 y Fs(V)1642 5235 y Fu(k)1687 5249 y Fx(1)1752 5235 y Fr(6)25 b Fv(\016)1891 5134 y Fq(\021)1987 5235 y Fr(>)2093 5173 y FA(1)p 2093 5214 V 2093 5297 a(2)2148 5235 y Fv(\026)2203 5196 y Fx(+)2203 5264 y Fs(\014)s(;N)2348 5235 y FA(\()p Fu(A)20 b(\\)g(B)s FA(\))15 b Fv(:)780 b FA(\(3.7\))118 5478 y Fn(Step)33 b(3)g(:)42 b(Surfac)-5 b(e)33 b(tension.)p 118 5510 989 4 v eop %%Page: 13 13 13 12 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(13)218 366 y FA(The)30 b(con\014gurations)g(in)f (the)i(ev)m(en)m(t)h Fu(A)19 b(\\)h(B)33 b FA(con)m(tain)e(+)f(and)g Fu(\000)h FA(closed)f(surfaces)g(whic)m(h)f(split)g(the)118 474 y(domain)g Fy(D)500 488 y Fs(N)603 474 y FA(in)m(to)h(3)g(regions.) 40 b(Let)31 b(\003)1432 441 y Ft(\000)1520 474 y FA(b)s(e)f(the)f (region)h(surrounded)d(b)m(y)j(the)g Fu(\000)f FA(surface,)h(\003)3323 441 y Fx(+)3412 474 y FA(b)s(e)f(the)118 582 y(region)k(outside)g(the)h (+)f(surface.)51 b(T)-8 b(o)34 b(ensure)e(the)i(uniqueness)d(of)j(the)g (decomp)s(osition,)f(w)m(e)h(c)m(ho)s(ose)118 696 y(the)k(+)f(surface)g (\(resp)g Fu(\000)p FA(\))h(in)e(eac)m(h)i Fj(R)1481 652 y Fs(i;)p Fx(+)1481 725 y Fs(N)1621 696 y FA(\(resp)g Fj(R)1932 652 y Fs(i;)p Ft(\000)1932 725 y Fs(N)2034 696 y FA(\))g(as)g(the)f(closest)h(surface)g(from)f(\()p Fv(R)3326 663 y Fs(i)3325 723 y(N)3392 696 y FA(\))3427 663 y Fs(c)3462 696 y FA(.)62 b(By)118 806 y(de\014nition,)25 b(the)h(con\014gurations)g(inside)e(\003)1596 774 y Ft(\000)1681 806 y FA(\(resp)i(\003)1968 774 y Fx(+)2027 806 y FA(\))g(are)h (surrounded)d(b)m(y)i Fu(\000)f FA(\(resp)h(+\))g(b)s(oundary)118 914 y(conditions.)39 b(Finally)29 b(\001)c(=)g Fy(D)1154 928 y Fs(N)1248 914 y Fu(n)20 b FA(\003)1376 881 y Fx(+)1456 914 y Fu([)g FA(\003)1600 881 y Ft(\000)1659 914 y FA(.)218 1022 y(W)-8 b(e)31 b(pro)s(ceed)f(no)m(w)h(to)g(ev)-5 b(aluate)31 b(the)g(RHS)e(of)38 b(\(3.7\))998 1241 y Fv(\026)1053 1203 y Fx(+)1053 1271 y Fs(\014)s(;N)1197 1241 y FA(\()q Fu(A)19 b(\\)h(B)s FA(\))40 b Fr(>)1692 1180 y FA(1)p 1650 1220 130 4 v 1650 1310 a Fv(Z)1719 1271 y Fx(+)1712 1338 y Fs(N)1849 1155 y Fq(X)1805 1357 y Fx(\003)1854 1338 y Fm(+)1904 1357 y Fs(;)p Fx(\003)1973 1338 y Fl(\000)2040 1241 y Fv(Z)2109 1203 y Fx(+)2102 1275 y(\003)2151 1256 y Fm(+)2206 1241 y Fv(Z)2275 1203 y Ft(\000)2268 1275 y Fx(\003)2317 1256 y Fl(\000)2373 1241 y Fv(Z)2442 1197 y Fx(+)p Fs(;)p Ft(\000)2435 1270 y Fx(\001)2591 1241 y Fv(;)118 1518 y FA(where)30 b Fv(Z)450 1485 y Fs(!)443 1545 y(D)537 1518 y FA(denotes)h(the)g(partition)e (function)g(on)h(the)h(domain)e Fv(D)k FA(with)c(b)s(oundary)f (conditions)h Fv(!)s FA(.)218 1626 y(By)h(using)f(the)i(spin)d(\015ip)h (symmetry)h(w)m(e)h(get)716 1879 y Fv(\026)771 1841 y Fx(+)771 1909 y Fs(\014)s(;N)916 1879 y FA(\()p Fu(A)20 b(\\)g(B)s FA(\))40 b Fr(>)g FA(min)1420 1940 y Fx(\001)1541 1724 y Fq( )1623 1815 y Fv(Z)1692 1771 y Fx(+)p Fs(;)p Ft(\000)1685 1844 y Fx(\001)p 1623 1858 203 4 v 1623 1954 a Fv(Z)1692 1909 y Fx(+)p Fs(;)p Fx(+)1685 1982 y(\001)1835 1724 y Fq(!)1974 1818 y FA(1)p 1932 1858 130 4 v 1932 1948 a Fv(Z)2001 1909 y Fx(+)1994 1976 y Fs(N)2131 1793 y Fq(X)2086 1995 y Fx(\003)2135 1976 y Fm(+)2186 1995 y Fs(;)p Fx(\003)2255 1976 y Fl(\000)2322 1879 y Fv(Z)2391 1841 y Fx(+)2384 1913 y(\003)2433 1894 y Fm(+)2488 1879 y Fv(Z)2557 1841 y Fx(+)2550 1913 y(\003)2599 1894 y Fl(\000)2655 1879 y Fv(Z)2724 1835 y Fx(+)p Fs(;)p Fx(+)2717 1908 y(\001)2872 1879 y Fv(:)578 b FA(\(3.8\))118 2156 y(The)23 b(minim)m(um)d(is)i(tak)m(en)i(o)m(v)m(er)h(the)e(sets)h (\001)e(whic)m(h)g(can)i(b)s(e)e(obtained)h(b)m(y)g(the)g(previous)f (construction.)118 2264 y(In)f(particular,)h(\001)g(should)e(con)m (tain)i(the)g(union)e(of)i(disjoin)m(t)e(domains)h(\001)2580 2231 y Fs(i)2629 2264 y FA(suc)m(h)h(that)g Fv(Q)3086 2231 y Fs(i)3086 2291 y(N)3179 2264 y Fu(\032)j FA(\001)3351 2231 y Fs(i)3404 2264 y Fu(\032)g Fv(R)3570 2231 y Fs(i)3569 2291 y(N)3636 2264 y FA(.)118 2372 y(It)31 b(remains)e(to)i(ev)-5 b(aluate)31 b(the)f(t)m(w)m(o)i(terms)e(in)g(the)g(RHS.)218 2588 y(The)f(partition)g(function)f Fv(Z)1207 2544 y Fx(+)p Fs(;)p Ft(\000)1200 2617 y Fx(\001)1370 2588 y FA(tak)m(es)k(in)m(to)d(accoun)m(t)j(the)e(in)m(teraction)g(on)g(b)s (oth)f(sides)g(of)h Fv(U)3468 2555 y Fs(\016)3458 2615 y(N)3525 2588 y FA(,)g(as)118 2702 y(w)m(ell)24 b(as)i(inside)d(eac)m (h)k(\001)933 2669 y Fs(i)960 2702 y FA(.)39 b(As)26 b(the)f(former)g(in)m(teraction)g(in)m(v)m(olv)m(es)h(only)e(the)i (spins)d(in)h(a)i(neigh)m(b)s(orho)s(o)s(d)118 2810 y(of)31 b Fv(U)294 2777 y Fs(\016)284 2837 y(N)351 2810 y FA(,)g(w)m(e)f (obtain)868 3082 y(min)914 3142 y Fx(\001)1045 3018 y Fv(Z)1114 2974 y Fx(+)p Fs(;)p Ft(\000)1107 3046 y Fx(\001)p 1045 3061 203 4 v 1045 3156 a Fv(Z)1114 3112 y Fx(+)p Fs(;)p Fx(+)1107 3185 y(\001)1282 3082 y Fr(>)40 b FA(exp)1547 3008 y Fq(\000)1609 3082 y Fu(\000)20 b Fv(\014)5 b(o)p FA(\()p Fv(\016)s FA(\))p Fv(N)1996 3044 y Fs(d)p Ft(\000)p Fx(1)2128 3008 y Fq(\001)2229 2968 y Fs(`)2185 2995 y Fq(Y)2186 3191 y Fs(i)p Fx(=1)2316 3082 y FA(min)2350 3149 y Fx(\001)2409 3130 y Fp(i)2493 3011 y Fv(Z)2562 2967 y Fx(+)p Fs(;)p Ft(\000)2555 3046 y Fx(\001)2614 3027 y Fp(i)p 2493 3061 V 2493 3156 a Fv(Z)2562 3112 y Fx(+)p Fs(;)p Fx(+)2555 3191 y(\001)2614 3172 y Fp(i)2720 3082 y Fv(;)118 3353 y FA(where)41 b(the)h(minim)m(um)d(is)i(tak)m(en)h (o)m(v)m(er)h(the)f(sets)g(\001)1978 3320 y Fs(i)2048 3353 y FA(suc)m(h)f(that)h Fv(Q)2544 3320 y Fs(i)2544 3380 y(N)2655 3353 y Fu(\032)i FA(\001)2846 3320 y Fs(i)2918 3353 y Fu(\032)g Fv(R)3103 3320 y Fs(i)3102 3380 y(N)3169 3353 y FA(.)74 b(Using)41 b(the)118 3461 y(de\014nition)28 b(\(2.2\))r(,)j(w)m(e)f(kno)m(w)h(that)690 3719 y(lim)15 b(inf)714 3779 y Fs(N)7 b Ft(!1)1051 3657 y FA(1)p 967 3698 214 4 v 967 3781 a Fv(N)1050 3755 y Fs(d)p Ft(\000)p Fx(1)1221 3719 y FA(min)1254 3786 y Fx(\001)1313 3767 y Fp(i)1403 3563 y Fq( )1475 3719 y FA(log)1618 3648 y Fv(Z)1687 3604 y Fx(+)p Fs(;)p Ft(\000)1680 3683 y Fx(\001)1739 3664 y Fp(i)p 1618 3698 203 4 v 1618 3793 a Fv(Z)1687 3749 y Fx(+)p Fs(;)p Fx(+)1680 3828 y(\001)1739 3809 y Fp(i)1830 3563 y Fq(!)1942 3719 y Fr(>)45 b Fu(\000)2164 3595 y Fq(Z)2229 3785 y Fk(b)2215 3801 y Fs(B)2271 3782 y Fp(i)2317 3719 y Fv(\034)2357 3734 y Fs(\014)2404 3719 y FA(\()n Fv(~)-43 b(n)2494 3733 y Fs(i)2522 3719 y FA(\))15 b Fv(d)p Fu(H)2697 3681 y Fx(\()p Fs(d)p Ft(\000)p Fx(1\))2696 3741 y Fs(x)2898 3719 y Fv(:)552 b FA(\(3.9\))118 3986 y(W)-8 b(e)32 b(used)d(the)i(fact)g(that)g(\001)1091 3953 y Fs(i)1149 3986 y FA(increases)f(as)h Fv(N)40 b FA(div)m(erges.)218 4201 y(In)30 b(the)h(last)g(term)g(in)e(the)j(RHS)e (of)38 b(\(3.8\))r(,)31 b(the)g(constrain)m(t)g(on)g(the)g(spins)e (along)i(the)g(set)h Fv(U)3427 4168 y Fs(\016)3417 4228 y(N)3515 4201 y FA(and)118 4314 y(on)e(the)f(sides)g(of)g Fv(R)789 4281 y Fs(i)788 4340 y(N)885 4314 y FA(parallel)f(to)f Fv(~)-42 b(n)1373 4328 y Fs(i)1430 4314 y FA(can)30 b(b)s(e)f(released) g(up)g(to)h(a)g(small)e(cost)i(wrt)f(the)h(surface)g(order.)118 4428 y(This)22 b(comes)i(from)f(the)h(fact)g(that)h(the)e(ev)m(en)m(t)i Fu(B)h FA(is)d(supp)s(orted)f(b)m(y)h(at)h(most)g Fv(c)p FA(\()p Fv(d;)15 b(\016)s FA(\))p Fv(N)3036 4395 y Fs(d)p Ft(\000)p Fx(1)3193 4428 y FA(edges)24 b(where)118 4536 y Fv(c)p FA(\()p Fv(d;)15 b(\016)s FA(\))32 b(v)-5 b(anishes)28 b(as)h Fv(\016)k FA(go)s(es)d(to)g(0.)41 b(Therefore)28 b(the)i(probabilit)m(y)d(of)i Fu(B)i FA(is)e(negligible)e(with)g(resp)s (ect)j(to)118 4644 y(a)h(surface)f(order.)744 4778 y(1)p 702 4819 130 4 v 702 4908 a Fv(Z)771 4870 y Fx(+)764 4937 y Fs(N)901 4754 y Fq(X)856 4956 y Fx(\003)905 4937 y Fm(+)956 4956 y Fs(;)p Fx(\003)1025 4937 y Fl(\000)1092 4840 y Fv(Z)1161 4802 y Fx(+)1154 4874 y(\003)1203 4855 y Fm(+)1258 4840 y Fv(Z)1327 4802 y Fx(+)1320 4874 y(\003)1369 4855 y Fl(\000)1425 4840 y Fv(Z)1494 4796 y Fx(+)p Fs(;)p Fx(+)1487 4869 y(\001)1652 4840 y Fr(>)41 b FA(exp)1918 4766 y Fq(\000)1979 4840 y Fu(\000)20 b Fv(\014)5 b(o)p FA(\()p Fv(\016)s FA(\))p Fv(N)2366 4802 y Fs(d)p Ft(\000)p Fx(1)2499 4766 y Fq(\001)2540 4840 y Fv(\026)2595 4802 y Fx(+)2595 4869 y Fs(\014)s(;N)2725 4766 y Fq(\000)2798 4817 y FA(~)2767 4840 y Fu(A)2839 4766 y Fq(\001)2896 4840 y Fv(;)118 5138 y FA(where)416 5115 y(~)385 5138 y Fu(A)34 b FA(is)g(the)h(ev)m(en)m(t)h(deduced)e(from)g Fu(A)g FA(b)m(y)h(spin)d(\015ip)h(symmetry)-8 b(,)36 b(i.e.)53 b(suc)m(h)35 b(that)g(there)g(are)g(in)118 5252 y(eac)m(h)28 b(set)f Fj(R)532 5208 y Fs(i;)p Fx(+)532 5280 y Fs(N)661 5252 y FA(and)f Fj(R)909 5208 y Fs(i;)p Ft(\000)909 5280 y Fs(N)1039 5252 y FA(a)h(+)f(surface)h(of)f(spins.)38 b(Using)25 b(the)i(P)m(eierls)f(argumen)m(t,)i(w)m(e)f(conclude)f(that) 118 5372 y Fv(\026)173 5334 y Fx(+)173 5402 y Fs(\014)s(;N)303 5372 y FA(\()369 5349 y(~)338 5372 y Fu(A)p FA(\))k(is)g(uniformly)d(b) s(ounded)h(from)i(b)s(elo)m(w)g(in)f Fv(N)10 b FA(.)p eop %%Page: 14 14 14 13 bop 118 45 a Fx(14)1460 b(T.)23 b(BODINEA)n(U)218 366 y FA(Th)m(us)29 b(inequalities)f(\(3.7\))r(,)i(\(3.8\))r(,)h (\(3.9\))h(imply)503 624 y(lim)15 b(inf)527 684 y Fs(N)7 b Ft(!1)864 562 y FA(1)p 780 603 214 4 v 780 686 a Fv(N)863 660 y Fs(d)p Ft(\000)p Fx(1)1034 624 y FA(log)16 b Fv(\026)1221 585 y Fx(+)1221 653 y Fs(\014)s(;N)1366 624 y FA(\()p Fu(A)k(\\)g(B)s FA(\))40 b Fr(>)61 b Fu(\000)1987 510 y Fs(`)1935 537 y Fq(X)1944 733 y Fs(i)p Fx(=1)2082 500 y Fq(Z)2147 689 y Fk(b)2132 706 y Fs(B)2188 687 y Fp(i)2235 624 y Fv(\034)2275 639 y Fs(\014)2322 624 y FA(\()n Fv(~)-43 b(n)2412 638 y Fs(i)2440 624 y FA(\))15 b Fv(d)p Fu(H)2615 586 y Fx(\()p Fs(d)p Ft(\000)p Fx(1\))2614 646 y Fs(x)2821 624 y Fu(\000)20 b Fv(o)p FA(\()p Fv(\016)s FA(\))15 b Fv(:)320 b FA(\(3.10\))118 870 y(This)29 b(concludes)g(the)i(pro)s (of)e(of)i(Prop)s(osition)d(3.2.)118 1071 y(3.4.)47 b FF(Upp)s(er)41 b(b)s(ound.)46 b FA(The)36 b(pro)s(of)f(of)h(Prop)s (osition)d(3.3)k(follo)m(ws)e(the)h(general)g(sc)m(heme)g(of)g(the)g Fy(L)3616 1038 y Fx(1)118 1179 y FA(Theory)-8 b(.)62 b(The)37 b(di\013eren)m(t)f(steps)i(will)c(b)s(e)j(recalled)f(and)h(mo) s(di\014ed)e(in)h(order)h(to)h(use)f(only)g(the)g(spin)118 1287 y(represen)m(tation.)67 b(First)38 b(the)h(b)s(oundary)e Fv(@)1640 1254 y Ft(\003)1680 1287 y Fv(v)42 b FA(is)c(appro)m (ximated;)43 b(this)38 b(enables)g(us)h(to)g(reduce)g(the)118 1395 y(pro)s(of)26 b(to)i(lo)s(cal)e(computations)h(in)f(small)f (regions.)39 b(Then)26 b(in)g(eac)m(h)i(region)f(w)m(e)g(lo)s(calize)g (the)g(in)m(terface)118 1503 y(on)33 b(the)f(mesoscopic)h(lev)m(el)g(b) m(y)f(using)f(the)i(minimal)d(section)j(argumen)m(t.)48 b(Finally)30 b(in)i(the)h(last)f(step,)118 1611 y(the)f(surface)f (tension)g(factor)h(is)e(computed.)118 1776 y Fn(Step)k(1)g(:)42 b(Appr)-5 b(oximation)36 b(pr)-5 b(o)g(c)g(e)g(dur)g(e.)p 118 1808 1366 4 v 218 1884 a FA(W)d(e)31 b(appro)m(ximate)g Fv(@)953 1851 y Ft(\003)993 1884 y Fv(v)i FA(with)c(a)i(\014nite)e(n)m (um)m(b)s(er)g(of)i(parallelepip)s(eds.)118 2057 y FF(Theorem)42 b(3.5.)j Fn(F)-7 b(or)40 b(any)g Fv(\016)i Fn(p)-5 b(ositive,)41 b(ther)-5 b(e)40 b(exists)f Fv(h)g Fn(p)-5 b(ositive)40 b(such)f(that)h(ther)-5 b(e)39 b(ar)-5 b(e)40 b Fv(`)e Fn(disjoint)118 2172 y(p)-5 b(ar)g(al)5 b(lelepip)-5 b(e)g(ds)726 2149 y Fq(b)709 2172 y Fv(R)779 2139 y Fx(1)818 2172 y Fv(;)15 b(:)g(:)g(:)i(;)1037 2149 y Fq(b)1020 2172 y Fv(R)1090 2139 y Fs(`)1151 2172 y Fn(include)-5 b(d)28 b(in)1615 2148 y Fq(b)1608 2172 y Fy(D)50 b Fn(with)29 b(b)-5 b(asis)2126 2149 y Fq(b)2107 2172 y Fv(B)2181 2139 y Fx(1)2220 2172 y Fv(;)15 b(:)g(:)g(:)i(;)2441 2149 y Fq(b)2422 2172 y Fv(B)2496 2139 y Fs(`)2556 2172 y Fn(of)28 b(size)g Fv(h)g Fn(and)h(height)f Fv(\016)s(h)p Fn(.)41 b(The)118 2286 y(b)-5 b(asis)355 2263 y Fq(b)336 2286 y Fv(B)410 2253 y Fs(i)469 2286 y Fn(divides)787 2263 y Fq(b)770 2286 y Fv(R)840 2253 y Fs(i)900 2286 y Fn(in)32 b(2)g(p)-5 b(ar)g(al)5 b(lelepip)-5 b(e)g(ds)1701 2263 y Fq(b)1684 2286 y Fv(R)1754 2253 y Fs(i;)p Fx(+)1888 2286 y Fn(and)2081 2263 y Fq(b)2064 2286 y Fv(R)2134 2253 y Fs(i;)p Ft(\000)2268 2286 y Fn(and)33 b(the)f(normal)h(to)3033 2263 y Fq(b)3014 2286 y Fv(B)3088 2253 y Fs(i)3147 2286 y Fn(is)f(denote)-5 b(d)33 b(by)116 2394 y Fv(~)-43 b(n)173 2408 y Fs(i)201 2394 y Fn(.)42 b(F)-7 b(urthermor)i(e,)35 b(the)e(p)-5 b(ar)g(al)5 b(lelepip)-5 b(e)g(ds)36 b(satisfy)e(the)f (fol)5 b(lowing)34 b(pr)-5 b(op)g(erties)231 2523 y Fq(Z)294 2712 y Fk(b)281 2729 y Fs(R)334 2710 y Fp(i)380 2646 y Fu(jX)483 2663 y Fk(b)470 2680 y Fs(R)523 2661 y Fp(i)555 2646 y FA(\()p Fv(x)p FA(\))20 b Fu(\000)g Fv(v)s FA(\()p Fv(x)p FA(\))p Fu(j)15 b Fv(dx)27 b Fr(6)e Fv(\016)19 b Fn(vol)q FA(\()1442 2623 y Fq(b)1425 2646 y Fv(R)1495 2609 y Fs(i)1523 2646 y FA(\))93 b(and)1891 2542 y Fq(\014)1891 2596 y(\014)1891 2651 y(\014)1987 2533 y Fs(`)1936 2560 y Fq(X)1945 2755 y Fs(i)p Fx(=1)2083 2523 y Fq(Z)2148 2712 y Fk(b)2133 2729 y Fs(B)2189 2710 y Fp(i)2235 2646 y Fv(\034)2275 2661 y Fs(\014)2322 2646 y FA(\()n Fv(~)-43 b(n)2412 2660 y Fs(i)2440 2646 y FA(\))15 b Fv(d)p Fu(H)2615 2609 y Fx(\()p Fs(d)p Ft(\000)p Fx(1\))2614 2669 y Fs(x)2821 2646 y Fu(\000)20 b(W)3002 2661 y Fs(\014)3049 2646 y FA(\()p Fv(v)s FA(\))3166 2542 y Fq(\014)3166 2596 y(\014)3166 2651 y(\014)3223 2646 y Fr(6)25 b Fv(\016)n(;)118 2918 y Fn(wher)-5 b(e)34 b Fu(X)453 2935 y Fk(b)440 2952 y Fs(R)493 2933 y Fp(i)549 2918 y FA(=)25 b(1)703 2935 y Fk(b)690 2952 y Fs(R)743 2933 y Fp(i;)p Fm(+)860 2918 y Fu(\000)20 b FA(1)1009 2935 y Fk(b)996 2952 y Fs(R)1049 2933 y Fp(i;)p Fl(\000)1180 2918 y Fn(and)34 b(the)f(volume)g(of)1941 2896 y Fq(b)1923 2918 y Fv(R)1993 2885 y Fs(i)2054 2918 y Fn(is)f(vol)q FA(\()2315 2896 y Fq(b)2298 2918 y Fv(R)2368 2885 y Fs(i)2396 2918 y FA(\))26 b(=)f Fv(\016)s(h)2648 2885 y Fs(d)2689 2918 y Fn(.)118 3093 y FA(The)j(pro)s(of)g(follo)m(ws) g(from)g(standard)f(argumen)m(ts)i(of)g(geometric)h(measure)e(theory)h (\(see)g(for)g(example)118 3201 y([Ce,)e(B1)q(]\).)40 b(Theorem)25 b(3.5)j(enables)d(us)h(to)h(decomp)s(ose)f(the)g(b)s (oundary)f(in)m(to)h(regular)f(sets)i(\(see)g(\014gure)118 3309 y(4\))k(so)g(that)g(it)f(will)d(b)s(e)j(enough)g(to)h(consider)f (ev)m(en)m(ts)h(of)g(the)g(t)m(yp)s(e)1080 3411 y Fq(\()1200 3505 y FA(1)p 1163 3545 120 4 v 1163 3629 a Fv(m)1243 3602 y Ft(\003)1292 3566 y Fu(M)1401 3580 y Fs(N)s(;K)1574 3566 y Fu(2)1702 3453 y Fs(`)1666 3480 y Fq(\\)1660 3675 y Fs(i)p Fx(=1)1804 3566 y Fu(V)7 b FA(\()1920 3543 y Fq(b)1902 3566 y Fv(R)1972 3529 y Fs(i)2001 3566 y Fv(;)15 b(\016)s FA(v)m(ol)q(\()2253 3543 y Fq(b)2236 3566 y Fv(R)2306 3529 y Fs(i)2334 3566 y FA(\)\))2404 3411 y Fq(\))2508 3566 y Fv(;)118 3839 y FA(where)30 b Fu(V)7 b FA(\()497 3816 y Fq(b)479 3839 y Fv(R)549 3806 y Fs(i)577 3839 y Fv(;)15 b(")p FA(\))32 b(is)d(the)i Fv(")p FA(-neigh)m(b)s(orho) s(o)s(d)e(of)h Fu(X)1799 3855 y Fk(b)1786 3872 y Fs(R)1839 3853 y Fp(i)675 4069 y Fu(V)7 b FA(\()790 4046 y Fq(b)773 4069 y Fv(R)843 4032 y Fs(i)871 4069 y Fv(;)15 b(")p FA(\))26 b(=)1110 3941 y Fq(\032)1179 4069 y Fv(v)1226 4032 y Ft(0)1274 4069 y Fu(2)f Fy(L)1415 4032 y Fx(1)1460 3996 y Fq(\000)1510 4046 y(b)1502 4069 y Fy(D)1568 3996 y Fq(\001)1640 3992 y(\014)1640 4047 y(\014)1776 3946 y(Z)1840 4135 y Fk(b)1827 4152 y Fs(R)1880 4133 y Fp(i)1926 4069 y Fu(j)p Fv(v)1998 4032 y Ft(0)2022 4069 y FA(\()p Fv(x)p FA(\))c Fu(\000)e(X)2333 4086 y Fk(b)2320 4103 y Fs(R)2373 4084 y Fp(i)2404 4069 y FA(\()p Fv(x)p FA(\))p Fu(j)c Fv(dx)27 b Fr(6)e Fv(")2830 3941 y Fq(\033)2914 4069 y Fv(:)218 4289 y FA(According)h(to)h(\(3.3\),)i(the)d(lo)s(cal)g (a)m(v)m(eraged)i(magnetization)f(can)g(b)s(e)f(replaced)f(b)m(y)i(the) f(mesoscopic)118 4397 y(phase)31 b(lab)s(els.)40 b(Therefore)31 b(Prop)s(osition)e(3.3)j(is)e(equiv)-5 b(alen)m(t)30 b(to)i(the)f(follo)m(wing)e(statemen)m(t)k(:)41 b(for)31 b(an)m(y)118 4505 y Fv(\016)f FA(p)s(ositiv)m(e,)c(there)g(exists)f Fv(K)1097 4519 y Fx(0)1162 4505 y FA(=)g Fv(K)1335 4519 y Fx(0)1375 4505 y FA(\()p Fv(\016)n(;)15 b(h)p FA(\),)29 b Fv(\020)1669 4519 y Fx(0)1733 4505 y FA(=)c Fv(\020)1869 4519 y Fx(0)1909 4505 y FA(\()p Fv(\016)n(;)15 b(h)p FA(\))28 b(suc)m(h)d(that)i(uniformly)22 b(in)j Fv(K)32 b Fr(>)25 b Fv(K)3323 4519 y Fx(0)3363 4505 y FA(,)i Fv(\020)k Fr(6)25 b Fv(\020)3622 4519 y Fx(0)288 4763 y FA(lim)15 b(sup)325 4840 y Fs(N)7 b Ft(!1)675 4701 y FA(1)p 591 4741 214 4 v 591 4825 a Fv(N)674 4798 y Fs(d)p Ft(\000)p Fx(1)845 4763 y FA(log)17 b Fv(\026)1033 4724 y Fx(+)1033 4792 y Fs(\014)s(;N)1177 4607 y Fq( )1249 4763 y Fv(u)1301 4718 y Fs(\020)1301 4791 y(N)s(;K)1474 4763 y Fu(2)1602 4649 y Fs(`)1566 4676 y Fq(\\)1560 4871 y Fs(i)p Fx(=1)1704 4763 y Fu(V)7 b FA(\()1820 4739 y Fq(b)1802 4762 y Fv(R)1872 4725 y Fs(i)1901 4763 y Fv(;)15 b(\016)s FA(v)m(ol)q(\()2154 4739 y Fq(b)2136 4762 y Fv(R)2206 4725 y Fs(i)2234 4763 y FA(\)\))2304 4607 y Fq(!)2417 4763 y Fr(6)46 b Fu(\000)19 b(W)2714 4778 y Fs(\014)2761 4763 y FA(\()p Fv(v)s FA(\))j(+)e Fv(C)7 b FA(\()p Fv(\014)e(;)15 b(v)s FA(\))p Fv(\016)n(:)3429 4760 y FA(\(3.11\))118 5111 y Fn(Step)33 b(2)g(:)42 b(Minimal)33 b(se)-5 b(ction)33 b(ar)-5 b(gument.)p 118 5143 1417 4 v 218 5243 a FA(F)d(ollo)m(wing,)33 b(the)h(notation)f(of)g(the)h (subsection)e(3.3,)j(w)m(e)f(consider)e(the)h(partition)f(\()p Fv(R)3204 5199 y Fs(i;)p Fx(+)3203 5272 y Fs(N)3307 5243 y Fv(;)15 b(R)3417 5199 y Fs(i;)p Ft(\000)3416 5272 y Fs(N)3520 5243 y FA(\))33 b(of)118 5357 y Fv(R)188 5324 y Fs(i)187 5384 y(N)254 5357 y FA(.)40 b(A)m(t)29 b(a)g(giv)m(en)f (mesoscopic)g(scale)g Fv(K)7 b FA(,)29 b(w)m(e)f(asso)s(ciate)h(to)g (an)m(y)f(spins)e(con\014guration)h(the)i(set)f(of)g Fn(b)-5 b(ad)118 5480 y FA(b)s(o)m(xes)28 b(whic)m(h)f(are)h(the)g(b)s (o)m(xes)g Fy(B)1229 5494 y Fs(K)1331 5480 y FA(in)m(tersecting)g Fv(R)1887 5447 y Fs(i)1886 5507 y(N)1981 5480 y FA(with)e(lab)s(el)g(0) i(and)g(the)g(ones)f(in)m(tersecting)h Fv(R)3559 5436 y Fs(i;)p Fx(+)3558 5509 y Fs(N)p eop %%Page: 15 15 15 14 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(15)877 283 y 16222704 9323399 0 0 45323632 25918013 startTexFig 877 283 a %%BeginDocument: ./pictures/approx_up.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: approx_up.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Mon Dec 18 16:25:49 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 689 394 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 394 moveto 0 0 lineto 689 0 lineto 689 394 lineto closepath clip newpath % Fill background color 0 0 moveto 689 0 lineto 689 394 lineto 0 394 lineto closepath 1.00 1.00 1.00 setrgbcolor fill -15.0 545.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline 7.500 slw n 900 8625 m 900 8622 l 900 8616 l 900 8605 l 900 8587 l 900 8564 l 900 8534 l 901 8499 l 901 8459 l 901 8417 l 901 8373 l 902 8329 l 902 8285 l 903 8243 l 903 8202 l 904 8164 l 904 8129 l 905 8097 l 906 8067 l 906 8039 l 907 8014 l 908 7991 l 909 7969 l 910 7949 l 911 7930 l 913 7913 l 915 7889 l 917 7866 l 919 7844 l 922 7824 l 925 7803 l 929 7783 l 933 7764 l 937 7744 l 941 7725 l 946 7706 l 950 7686 l 955 7667 l 960 7647 l 966 7626 l 971 7606 l 976 7584 l 982 7561 l 988 7538 l 992 7518 l 996 7498 l 1001 7477 l 1006 7454 l 1011 7430 l 1016 7405 l 1021 7379 l 1026 7351 l 1032 7323 l 1037 7295 l 1043 7265 l 1048 7236 l 1054 7206 l 1059 7177 l 1064 7148 l 1069 7119 l 1074 7091 l 1078 7064 l 1083 7038 l 1087 7013 l 1090 6990 l 1094 6967 l 1097 6946 l 1100 6925 l 1104 6899 l 1107 6874 l 1110 6850 l 1112 6827 l 1115 6805 l 1117 6783 l 1119 6762 l 1120 6741 l 1122 6721 l 1123 6702 l 1123 6683 l 1124 6665 l 1124 6647 l 1125 6630 l 1125 6613 l 1125 6596 l 1125 6579 l 1125 6563 l 1125 6547 l 1125 6530 l 1125 6513 l 1125 6495 l 1125 6476 l 1126 6457 l 1126 6436 l 1127 6415 l 1128 6394 l 1128 6372 l 1130 6349 l 1131 6327 l 1133 6305 l 1134 6283 l 1136 6262 l 1139 6241 l 1141 6221 l 1144 6201 l 1147 6182 l 1150 6163 l 1154 6142 l 1159 6121 l 1164 6099 l 1169 6078 l 1175 6056 l 1182 6034 l 1189 6012 l 1197 5990 l 1205 5968 l 1214 5946 l 1223 5925 l 1232 5905 l 1241 5885 l 1250 5866 l 1259 5849 l 1269 5832 l 1278 5816 l 1288 5800 l 1296 5786 l 1305 5773 l 1315 5759 l 1325 5746 l 1335 5732 l 1346 5717 l 1358 5702 l 1371 5687 l 1384 5672 l 1398 5656 l 1412 5639 l 1427 5622 l 1443 5605 l 1459 5588 l 1475 5570 l 1492 5552 l 1509 5533 l 1526 5515 l 1544 5495 l 1563 5475 l 1579 5457 l 1595 5439 l 1613 5420 l 1631 5400 l 1649 5379 l 1669 5357 l 1689 5334 l 1709 5311 l 1730 5287 l 1751 5262 l 1772 5238 l 1793 5212 l 1814 5187 l 1834 5163 l 1854 5138 l 1873 5114 l 1891 5091 l 1908 5068 l 1924 5046 l 1939 5025 l 1953 5005 l 1965 4986 l 1977 4968 l 1988 4950 l 2001 4925 l 2013 4901 l 2024 4878 l 2032 4856 l 2040 4834 l 2046 4813 l 2051 4794 l 2056 4775 l 2059 4757 l 2063 4740 l 2066 4725 l 2069 4710 l 2073 4697 l 2077 4685 l 2082 4673 l 2088 4663 l 2096 4650 l 2106 4638 l 2118 4627 l 2131 4615 l 2146 4603 l 2163 4592 l 2180 4582 l 2198 4572 l 2217 4564 l 2235 4556 l 2252 4550 l 2269 4545 l 2285 4540 l 2300 4538 l 2314 4536 l 2329 4535 l 2342 4535 l 2356 4536 l 2370 4538 l 2383 4541 l 2397 4544 l 2409 4549 l 2422 4554 l 2433 4560 l 2444 4567 l 2455 4573 l 2465 4580 l 2475 4588 l 2485 4595 l 2495 4603 l 2505 4612 l 2516 4621 l 2528 4630 l 2540 4640 l 2552 4650 l 2564 4660 l 2577 4670 l 2589 4679 l 2601 4688 l 2613 4697 l 2625 4705 l 2638 4713 l 2650 4720 l 2663 4727 l 2677 4734 l 2691 4741 l 2707 4747 l 2723 4754 l 2739 4761 l 2756 4767 l 2772 4773 l 2789 4779 l 2805 4785 l 2820 4790 l 2835 4795 l 2850 4800 l 2863 4804 l 2876 4809 l 2890 4813 l 2904 4817 l 2919 4821 l 2935 4824 l 2952 4827 l 2969 4829 l 2987 4830 l 3006 4831 l 3025 4830 l 3044 4829 l 3064 4826 l 3084 4823 l 3104 4818 l 3125 4813 l 3141 4807 l 3158 4802 l 3175 4795 l 3193 4788 l 3212 4780 l 3232 4771 l 3253 4762 l 3274 4752 l 3296 4741 l 3318 4730 l 3341 4718 l 3364 4706 l 3387 4694 l 3410 4682 l 3432 4669 l 3454 4657 l 3476 4645 l 3497 4633 l 3517 4621 l 3537 4610 l 3556 4599 l 3575 4588 l 3595 4576 l 3616 4564 l 3636 4552 l 3657 4540 l 3677 4528 l 3698 4516 l 3719 4503 l 3740 4491 l 3760 4479 l 3781 4468 l 3801 4456 l 3820 4445 l 3839 4435 l 3857 4425 l 3874 4415 l 3891 4406 l 3907 4397 l 3922 4390 l 3936 4382 l 3950 4375 l 3969 4365 l 3988 4356 l 4007 4348 l 4026 4340 l 4045 4332 l 4064 4324 l 4082 4318 l 4100 4312 l 4117 4306 l 4133 4301 l 4148 4297 l 4162 4293 l 4175 4290 l 4188 4288 l 4202 4285 l 4216 4283 l 4230 4281 l 4244 4280 l 4259 4279 l 4273 4278 l 4287 4279 l 4301 4280 l 4314 4281 l 4327 4283 l 4338 4285 l 4350 4288 l 4359 4290 l 4368 4292 l 4377 4295 l 4388 4298 l 4399 4302 l 4412 4305 l 4427 4309 l 4442 4313 l 4460 4316 l 4479 4320 l 4499 4323 l 4521 4327 l 4544 4330 l 4569 4333 l 4596 4335 l 4625 4338 l 4644 4339 l 4664 4340 l 4685 4341 l 4708 4342 l 4731 4343 l 4756 4343 l 4782 4344 l 4809 4344 l 4837 4344 l 4865 4344 l 4895 4344 l 4925 4344 l 4955 4343 l 4986 4342 l 5016 4341 l 5047 4340 l 5076 4338 l 5106 4336 l 5135 4334 l 5163 4332 l 5190 4329 l 5216 4326 l 5242 4323 l 5266 4320 l 5290 4316 l 5313 4313 l 5339 4308 l 5364 4302 l 5389 4296 l 5413 4290 l 5438 4284 l 5462 4276 l 5485 4269 l 5509 4261 l 5532 4253 l 5555 4244 l 5577 4236 l 5599 4227 l 5620 4218 l 5641 4210 l 5661 4201 l 5681 4193 l 5699 4185 l 5718 4177 l 5736 4170 l 5753 4163 l 5770 4156 l 5788 4150 l 5807 4143 l 5826 4137 l 5846 4131 l 5866 4125 l 5887 4119 l 5909 4114 l 5931 4109 l 5953 4104 l 5976 4100 l 5998 4096 l 6021 4093 l 6043 4090 l 6065 4088 l 6086 4086 l 6107 4085 l 6127 4085 l 6146 4085 l 6165 4085 l 6183 4086 l 6200 4088 l 6221 4090 l 6242 4093 l 6263 4097 l 6285 4102 l 6306 4108 l 6327 4114 l 6348 4121 l 6368 4128 l 6388 4136 l 6407 4144 l 6425 4152 l 6442 4159 l 6458 4167 l 6473 4174 l 6487 4181 l 6500 4188 l 6513 4194 l 6525 4200 l 6538 4206 l 6550 4212 l 6563 4219 l 6577 4225 l 6591 4231 l 6605 4238 l 6620 4244 l 6635 4250 l 6651 4256 l 6667 4263 l 6684 4269 l 6701 4275 l 6719 4281 l 6738 4288 l 6753 4293 l 6770 4298 l 6788 4304 l 6807 4310 l 6828 4315 l 6849 4321 l 6871 4327 l 6894 4333 l 6918 4339 l 6943 4345 l 6967 4350 l 6992 4355 l 7017 4360 l 7041 4364 l 7065 4367 l 7088 4370 l 7111 4372 l 7133 4374 l 7154 4375 l 7175 4375 l 7196 4375 l 7216 4374 l 7236 4372 l 7257 4370 l 7278 4367 l 7300 4363 l 7321 4359 l 7343 4354 l 7365 4349 l 7388 4343 l 7410 4337 l 7432 4330 l 7454 4324 l 7475 4317 l 7497 4310 l 7518 4303 l 7539 4296 l 7559 4289 l 7579 4282 l 7600 4275 l 7621 4268 l 7642 4261 l 7664 4254 l 7687 4247 l 7710 4240 l 7735 4233 l 7759 4226 l 7785 4220 l 7810 4213 l 7836 4207 l 7861 4201 l 7887 4196 l 7911 4191 l 7935 4187 l 7959 4183 l 7981 4180 l 8003 4178 l 8023 4176 l 8043 4175 l 8063 4175 l 8086 4176 l 8109 4177 l 8131 4179 l 8153 4183 l 8175 4187 l 8197 4192 l 8218 4197 l 8238 4203 l 8257 4210 l 8275 4216 l 8291 4223 l 8306 4229 l 8319 4235 l 8330 4240 l 8341 4245 l 8350 4250 l 8359 4255 l 8367 4259 l 8374 4263 l 8380 4266 l 8385 4270 l 8390 4273 l 8393 4277 l 8396 4281 l 8398 4285 l 8399 4289 l 8399 4294 l 8400 4300 l 8400 4306 l 8400 4313 l 8400 4322 l 8400 4333 l 8400 4345 l 8400 4358 l 8400 4373 l 8400 4388 l 8400 4402 l 8400 4417 l 8400 4430 l 8400 4442 l 8400 4453 l 8400 4463 l 8400 4477 l 8400 4489 l 8400 4498 l 8400 4507 l 8400 4515 l 8400 4525 l 8400 4533 l 8400 4542 l 8401 4553 l 8403 4565 l 8405 4578 l 8409 4593 l 8414 4607 l 8420 4622 l 8428 4636 l 8438 4650 l 8445 4660 l 8454 4670 l 8465 4680 l 8476 4690 l 8488 4701 l 8502 4711 l 8516 4722 l 8530 4731 l 8545 4741 l 8559 4749 l 8574 4757 l 8587 4764 l 8600 4770 l 8613 4775 l 8627 4780 l 8641 4785 l 8655 4789 l 8669 4792 l 8684 4795 l 8698 4797 l 8712 4798 l 8726 4799 l 8739 4800 l 8752 4800 l 8763 4800 l 8775 4800 l 8787 4800 l 8798 4800 l 8811 4800 l 8824 4800 l 8838 4800 l 8852 4800 l 8866 4800 l 8881 4800 l 8895 4800 l 8909 4800 l 8923 4800 l 8938 4800 l 8950 4800 l 8963 4800 l 8977 4801 l 8992 4802 l 9007 4803 l 9024 4805 l 9041 4809 l 9058 4813 l 9076 4818 l 9094 4825 l 9111 4832 l 9128 4841 l 9145 4851 l 9163 4863 l 9175 4872 l 9187 4881 l 9200 4892 l 9213 4904 l 9227 4918 l 9241 4932 l 9256 4947 l 9271 4963 l 9286 4980 l 9302 4998 l 9317 5016 l 9333 5035 l 9349 5054 l 9364 5073 l 9379 5093 l 9394 5112 l 9408 5131 l 9422 5150 l 9436 5169 l 9450 5188 l 9463 5205 l 9475 5222 l 9488 5240 l 9501 5259 l 9514 5278 l 9528 5298 l 9541 5318 l 9555 5339 l 9569 5361 l 9583 5383 l 9597 5405 l 9610 5428 l 9624 5451 l 9637 5473 l 9649 5496 l 9662 5518 l 9673 5541 l 9685 5563 l 9695 5585 l 9706 5607 l 9715 5628 l 9725 5650 l 9733 5670 l 9742 5691 l 9750 5712 l 9758 5733 l 9766 5756 l 9775 5779 l 9783 5802 l 9791 5826 l 9799 5851 l 9807 5876 l 9815 5901 l 9823 5927 l 9831 5952 l 9839 5978 l 9847 6003 l 9855 6028 l 9862 6053 l 9870 6077 l 9877 6101 l 9884 6124 l 9891 6147 l 9898 6169 l 9905 6191 l 9913 6213 l 9920 6236 l 9928 6259 l 9937 6283 l 9945 6307 l 9954 6332 l 9963 6357 l 9973 6382 l 9982 6408 l 9992 6433 l 10001 6460 l 10011 6486 l 10020 6512 l 10030 6538 l 10039 6563 l 10048 6588 l 10056 6613 l 10065 6637 l 10072 6661 l 10080 6683 l 10087 6706 l 10094 6728 l 10100 6750 l 10106 6770 l 10111 6790 l 10116 6811 l 10121 6832 l 10126 6854 l 10131 6876 l 10136 6900 l 10141 6923 l 10145 6948 l 10149 6974 l 10153 7000 l 10157 7026 l 10161 7054 l 10164 7081 l 10168 7109 l 10171 7138 l 10174 7167 l 10176 7196 l 10178 7225 l 10181 7254 l 10183 7284 l 10184 7313 l 10186 7344 l 10188 7375 l 10189 7399 l 10190 7423 l 10190 7449 l 10191 7475 l 10192 7503 l 10193 7532 l 10193 7562 l 10194 7594 l 10195 7628 l 10195 7665 l 10196 7703 l 10196 7744 l 10197 7786 l 10197 7831 l 10197 7878 l 10198 7927 l 10198 7977 l 10198 8027 l 10199 8078 l 10199 8127 l 10199 8174 l 10199 8219 l 10200 8260 l 10200 8296 l 10200 8326 l 10200 8351 l 10200 8370 l 10200 8384 l 10200 8393 l 10200 8398 l 10200 8400 l gs col7 0.90 shd ef gr gs col0 s gr % Polyline [60] 0 sd n 1185 5295 m 5100 3825 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 5685 3900 m 9510 4515 l gs col0 s gr [] 0 sd % Polyline gs clippath 3009 3937 m 2952 3953 l 2992 4099 l 2989 3976 l 3050 4083 l cp eoclip n 3150 4545 m 2985 3960 l gs col0 s gr gr % arrowhead n 3050 4083 m 2989 3976 l 2992 4099 l col0 s % Polyline gs clippath 1136 4813 m 1188 4782 l 1111 4652 l 1147 4771 l 1060 4683 l cp eoclip n 480 3645 m 1155 4785 l gs col0 s gr gr % arrowhead n 1060 4683 m 1147 4771 l 1111 4652 l col0 s % Polyline gs clippath 1501 5921 m 1460 5877 l 1350 5982 l 1458 5921 l 1392 6025 l cp eoclip n 435 6900 m 1470 5910 l gs col0 s gr gr % arrowhead n 1392 6025 m 1458 5921 l 1350 5982 l col0 s % Polyline gs clippath 9550 3241 m 9559 3182 l 9409 3161 l 9524 3208 l 9400 3220 l cp 6004 2668 m 5995 2727 l 6145 2748 l 6031 2702 l 6154 2689 l cp eoclip n 6015 2700 m 9540 3210 l gs col0 s gr gr % arrowhead n 6154 2689 m 6031 2702 l 6145 2748 l col0 s % arrowhead n 9400 3220 m 9524 3208 l 9409 3161 l col0 s % Polyline gs clippath 9657 4524 m 9716 4534 l 9743 4386 l 9693 4499 l 9684 4375 l cp 9857 3740 m 9798 3730 l 9771 3878 l 9822 3766 l 9830 3889 l cp eoclip n 9825 3750 m 9690 4515 l gs col0 s gr gr % arrowhead n 9830 3889 m 9822 3766 l 9771 3878 l col0 s % arrowhead n 9684 4375 m 9693 4499 l 9743 4386 l col0 s % Polyline 30.000 slw n 1121 4227 m 4531 3056 l 5111 4758 l 1708 5932 l 1121 4227 l cp gs col0 s gr % Polyline n 5910 3120 m 9481 3626 l 9226 5406 l 5665 4906 l 5910 3120 l cp gs col0 s gr % Polyline 0.000 slw n 825 7575 m 3225 7617 l 3204 8817 l 804 8775 l 825 7575 l cp gs col7 1.00 shd ef gr % Polyline n 906 7001 m 3189 7743 l 2817 8884 l 535 8141 l 906 7001 l cp gs col7 1.00 shd ef gr % Polyline n 3000 7575 m 5400 7575 l 5400 8775 l 3000 8775 l 3000 7575 l cp gs col7 1.00 shd ef gr % Polyline n 5325 7425 m 7725 7425 l 7725 8625 l 5325 8625 l 5325 7425 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9075 7350 m 11475 7350 l 11475 8550 l 9075 8550 l 9075 7350 l cp gs col7 1.00 shd ef gr % Polyline n 9150 7200 m 11550 7200 l 11550 8400 l 9150 8400 l 9150 7200 l cp gs col7 1.00 shd ef gr % Polyline n 9150 7200 m 11550 7200 l 11550 8400 l 9150 8400 l 9150 7200 l cp gs col7 1.00 shd ef gr % Polyline n 8492 7569 m 10609 6441 l 11175 7500 l 9057 8628 l 8492 7569 l cp gs col7 1.00 shd ef gr % Polyline n 7588 7717 m 9971 7430 l 10117 8618 l 7734 8910 l 7588 7717 l cp gs col7 1.00 shd ef gr $F2psEnd rs %%EndDocument endTexFig 2274 273 a FC(h)2639 597 y Fm(1)p 2639 611 31 4 v 2639 653 a(2)2679 628 y FC(\016)s(h)2983 864 y Fh(f)p FC(v)25 b FE(=)c(1)p Fh(g)1802 982 y(f)p FC(v)k FE(=)c Fh(\000)p FE(1)p Fh(g)1399 580 y FC(~)-37 b(n)1446 588 y Fp(i)1771 491 y Fi(b)1755 510 y FC(B)1817 478 y Fp(i)824 467 y Fi(b)810 486 y FC(R)869 454 y Fp(i;)p Fm(+)777 1058 y Fi(b)763 1076 y FC(R)822 1045 y Fp(i;)p Fl(\000)1117 1709 y FD(Figure)28 b(4.)38 b FE(Appro)n(ximation)25 b(b)n(y)f(parallelepip)r(eds.)118 1962 y FA(\(resp)36 b Fv(R)422 1918 y Fs(i;)p Ft(\000)421 1991 y Fs(N)525 1962 y FA(\))g(lab)s(eled)f(b)m(y)h Fu(\000)p FA(1)h(\(resp)f(1\).)59 b(F)-8 b(or)37 b(an)m(y)g(in)m(teger)g Fv(j)5 b FA(,)38 b(w)m(e)f(set)2662 1940 y Fq(b)2643 1962 y Fv(B)2717 1930 y Fs(i;j)2832 1962 y FA(=)2957 1940 y Fq(b)2938 1962 y Fv(B)3012 1930 y Fs(i)3064 1962 y FA(+)24 b Fv(j)d(c)3256 1977 y Fs(d)3307 1927 y(N)p 3307 1942 65 4 v 3307 1994 a(K)3393 1962 y Fv(~)-42 b(n)3451 1976 y Fs(i)3515 1962 y FA(and)118 2070 y(de\014ne)782 2231 y Fv(B)856 2186 y Fs(i;j)851 2259 y(N)961 2231 y FA(=)1057 2157 y Fq(\010)1110 2231 y Fv(j)1152 2193 y Ft(0)1201 2231 y Fu(2)25 b Fv(R)1357 2193 y Fs(i)1356 2253 y(N)1454 2231 y Fu(j)30 b(9)p Fv(x)25 b Fu(2)1742 2208 y Fq(b)1723 2231 y Fv(B)1797 2193 y Fs(i;j)1876 2231 y Fv(;)198 b Fu(k)p Fv(j)2186 2193 y Ft(0)2230 2231 y Fu(\000)20 b Fv(N)10 b(x)p Fu(k)2501 2245 y Fx(1)2566 2231 y Fr(6)25 b FA(10)2752 2157 y Fq(\011)2806 2231 y Fv(:)118 2400 y FA(The)f(sections)g Fu(B)695 2367 y Fs(i)692 2426 y(j)752 2400 y FA(of)h(the)f(parallelepip)s(ed)d Fv(R)1648 2367 y Fs(i)1647 2427 y(N)1738 2400 y FA(are)k(de\014ned)e (as)h(the)h(smallest)e(connected)i(set)g(of)f(b)s(o)m(xes)118 2535 y Fy(B)173 2549 y Fs(K)276 2535 y FA(in)m(tersecting)30 b Fv(B)838 2491 y Fs(i;j)833 2563 y(N)917 2535 y FA(.)41 b(The)29 b(parameter)g Fv(c)1641 2550 y Fs(d)1712 2535 y FA(is)f(c)m(hosen)i(suc)m(h)f(that)h(the)g Fu(B)2711 2502 y Fs(i)2708 2560 y(j)2773 2535 y FA(are)g(disjoin)m(t)e(surfaces)h (of)118 2660 y(b)s(o)m(xes.)41 b(F)-8 b(or)31 b Fv(j)36 b FA(p)s(ositiv)m(e,)30 b(let)g Fv(n)1188 2622 y Fx(+)1188 2687 y Fs(i)1247 2660 y FA(\()p Fv(j)5 b FA(\))31 b(b)s(e)f(the)h(n)m (um)m(b)s(er)e(of)h Fn(b)-5 b(ad)32 b FA(b)s(o)m(xes)e(in)f Fu(B)2685 2627 y Fs(i)2682 2685 y(j)2749 2660 y FA(and)g(de\014ne)986 2891 y Fv(n)1041 2853 y Fx(+)1041 2918 y Fs(i)1125 2891 y FA(=)24 b(min)1387 2763 y Fq(\032)1455 2891 y Fv(n)1510 2853 y Fx(+)1510 2918 y Fs(i)1569 2891 y FA(\()p Fv(j)5 b FA(\))27 b(:)207 b(0)26 b Fv(<)f(j)30 b(<)2295 2829 y(\016)s(h)p 2280 2870 126 4 v 2280 2953 a FA(2)p Fv(c)2364 2968 y Fs(d)2426 2829 y Fv(K)p 2426 2870 84 4 v 2426 2953 a(N)2519 2763 y Fq(\033)2603 2891 y Fv(:)118 3111 y FA(Call)e Fv(j)351 3078 y Fx(+)440 3111 y FA(the)i(smallest)e(lo)s (cation)i(where)e(the)i(minim)m(um)d(is)h(ac)m(hiev)m(ed)j(and)d (de\014ne)h(the)h(minimal)c(sec-)118 3225 y(tion)j(in)g Fv(R)480 3181 y Fs(i;)p Fx(+)479 3254 y Fs(N)582 3225 y FA(as)h Fu(B)756 3192 y Fs(i)753 3257 y(j)786 3238 y Fm(+)840 3225 y FA(.)40 b(F)-8 b(or)31 b Fv(j)k FA(negativ)m(e,)d(w)m (e)e(denote)g(b)m(y)g Fu(B)2138 3192 y Fs(i)2135 3257 y(j)2168 3238 y Fl(\000)2253 3225 y FA(the)g(minimal)c(section)k(in)f Fv(R)3240 3181 y Fs(i;)p Ft(\000)3239 3254 y Fs(N)3372 3225 y FA(and)g Fv(n)3603 3187 y Ft(\000)3603 3252 y Fs(i)118 3355 y FA(the)i(n)m(um)m(b)s(er)e(of)h Fn(b)-5 b(ad)32 b FA(b)s(o)m(xes)e(in)f Fu(B)1289 3322 y Fs(i)1286 3388 y(j)1319 3369 y Fl(\000)1405 3355 y FA(\(see)i(\014gure)f(5\).)995 3582 y 14358033 13052758 0 0 50586173 45586759 startTexFig 995 3582 a %%BeginDocument: ./pictures/section.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: section.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Fri Dec 15 21:00:33 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 769 693 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 693 moveto 0 0 lineto 769 0 lineto 769 693 lineto closepath clip newpath % Fill background color 0 0 moveto 769 0 lineto 769 693 lineto 0 693 lineto closepath 1.00 1.00 1.00 setrgbcolor fill 2.0 641.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline n 300 600 m 12300 600 l 12300 1500 l 300 1500 l cp gs col7 0.75 shd ef gr % Polyline 7.500 slw [30] 0 sd n 300 8400 m 12300 8400 l 12300 9300 l 300 9300 l cp gs col7 0.75 shd ef gr gs col0 s gr [] 0 sd % Polyline 0.000 slw n 10725 2163 m 10725 2180 l 10725 2197 l 10725 2214 l 10726 2231 l 10727 2249 l 10728 2267 l 10730 2284 l 10733 2301 l 10736 2318 l 10740 2333 l 10744 2348 l 10750 2362 l 10756 2375 l 10763 2388 l 10770 2400 l 10779 2412 l 10790 2423 l 10801 2435 l 10814 2447 l 10828 2458 l 10843 2468 l 10858 2478 l 10874 2486 l 10889 2494 l 10905 2500 l 10920 2505 l 10935 2510 l 10950 2513 l 10963 2514 l 10976 2515 l 10989 2515 l 11003 2514 l 11017 2513 l 11032 2510 l 11046 2506 l 11061 2500 l 11075 2494 l 11089 2487 l 11103 2479 l 11116 2470 l 11128 2460 l 11140 2449 l 11152 2437 l 11163 2425 l 11172 2413 l 11181 2400 l 11191 2386 l 11200 2372 l 11209 2356 l 11218 2339 l 11227 2321 l 11235 2303 l 11243 2284 l 11251 2265 l 11258 2246 l 11264 2227 l 11270 2209 l 11275 2191 l 11279 2173 l 11282 2157 l 11285 2141 l 11288 2125 l 11289 2110 l 11290 2095 l 11290 2080 l 11290 2065 l 11288 2050 l 11286 2035 l 11283 2021 l 11279 2006 l 11274 1991 l 11268 1976 l 11260 1962 l 11252 1949 l 11244 1935 l 11234 1923 l 11224 1910 l 11212 1898 l 11200 1886 l 11188 1875 l 11174 1864 l 11159 1852 l 11142 1840 l 11125 1829 l 11106 1817 l 11087 1805 l 11066 1794 l 11045 1783 l 11023 1773 l 11002 1763 l 10980 1755 l 10959 1747 l 10938 1740 l 10919 1735 l 10900 1731 l 10882 1727 l 10866 1726 l 10850 1725 l 10833 1726 l 10817 1728 l 10802 1732 l 10788 1737 l 10774 1743 l 10761 1750 l 10748 1759 l 10737 1768 l 10727 1777 l 10718 1787 l 10710 1796 l 10703 1806 l 10698 1815 l 10693 1823 l 10690 1831 l 10688 1838 l 10685 1849 l 10685 1859 l 10687 1868 l 10691 1877 l 10696 1886 l 10702 1897 l 10708 1910 l 10713 1925 l 10715 1936 l 10717 1948 l 10719 1961 l 10720 1976 l 10721 1993 l 10722 2011 l 10723 2030 l 10724 2050 l 10724 2070 l 10725 2089 l 10725 2108 l 10725 2127 l 10725 2145 l cp gs col7 0.90 shd ef gr % Polyline 30.000 slw n 300 0 m 12300 0 l 12300 9600 l 300 9600 l cp gs col0 s gr % Polyline 0.000 slw n 8775 2625 m 8785 2649 l 8796 2671 l 8806 2691 l 8815 2707 l 8822 2721 l 8828 2732 l 8833 2741 l 8838 2750 l 8842 2758 l 8848 2767 l 8855 2777 l 8864 2789 l 8876 2803 l 8890 2818 l 8907 2835 l 8925 2850 l 8937 2859 l 8949 2866 l 8960 2872 l 8970 2877 l 8979 2881 l 8986 2885 l 8992 2888 l 8997 2891 l 9002 2894 l 9006 2896 l 9009 2898 l 9013 2900 l 9016 2902 l 9019 2903 l 9022 2903 l 9026 2903 l 9030 2902 l 9035 2901 l 9041 2897 l 9047 2892 l 9054 2885 l 9061 2876 l 9068 2864 l 9075 2850 l 9082 2827 l 9088 2803 l 9093 2779 l 9097 2756 l 9101 2735 l 9104 2717 l 9107 2700 l 9110 2684 l 9113 2669 l 9115 2654 l 9116 2638 l 9117 2620 l 9116 2601 l 9113 2579 l 9109 2555 l 9101 2529 l 9090 2501 l 9075 2475 l 9057 2452 l 9037 2433 l 9018 2420 l 8999 2410 l 8982 2403 l 8966 2400 l 8952 2399 l 8938 2399 l 8925 2400 l 8912 2402 l 8898 2403 l 8884 2404 l 8868 2405 l 8851 2405 l 8832 2404 l 8813 2402 l 8793 2401 l 8775 2400 l 8763 2401 l 8753 2402 l 8746 2404 l 8741 2406 l 8739 2408 l 8738 2410 l 8739 2412 l 8740 2414 l 8743 2415 l 8746 2417 l 8750 2419 l 8754 2421 l 8758 2423 l 8761 2425 l 8765 2428 l 8768 2432 l 8770 2436 l 8772 2442 l 8774 2448 l 8775 2456 l 8775 2465 l 8775 2475 l 8775 2494 l 8774 2510 l 8772 2522 l 8769 2530 l 8766 2535 l 8762 2538 l 8759 2541 l 8757 2546 l 8757 2556 l 8759 2572 l 8765 2596 l cp gs col7 1.00 shd ef gr % Polyline n 3013 3700 m 3001 3714 l 2991 3728 l 2981 3743 l 2973 3759 l 2965 3775 l 2959 3792 l 2953 3809 l 2948 3827 l 2945 3846 l 2942 3864 l 2941 3883 l 2940 3901 l 2940 3920 l 2942 3938 l 2943 3956 l 2946 3973 l 2949 3990 l 2953 4006 l 2958 4022 l 2963 4038 l 2969 4055 l 2975 4072 l 2983 4089 l 2991 4106 l 3000 4124 l 3010 4142 l 3021 4160 l 3032 4177 l 3044 4195 l 3057 4212 l 3070 4229 l 3083 4245 l 3096 4260 l 3109 4274 l 3123 4288 l 3136 4301 l 3149 4313 l 3163 4325 l 3176 4336 l 3190 4347 l 3205 4358 l 3220 4368 l 3236 4379 l 3253 4388 l 3271 4398 l 3289 4406 l 3309 4415 l 3329 4422 l 3349 4429 l 3370 4434 l 3391 4439 l 3412 4443 l 3434 4446 l 3455 4448 l 3477 4450 l 3500 4450 l 3521 4450 l 3543 4449 l 3565 4447 l 3589 4445 l 3613 4441 l 3639 4437 l 3664 4433 l 3691 4427 l 3717 4421 l 3743 4415 l 3769 4407 l 3794 4399 l 3818 4391 l 3841 4382 l 3863 4373 l 3883 4364 l 3902 4355 l 3920 4345 l 3936 4335 l 3950 4325 l 3964 4313 l 3978 4301 l 3989 4288 l 4000 4275 l 4009 4260 l 4018 4246 l 4025 4230 l 4031 4214 l 4036 4198 l 4040 4182 l 4044 4166 l 4046 4150 l 4048 4134 l 4049 4119 l 4050 4104 l 4050 4090 l 4050 4076 l 4050 4063 l 4050 4045 l 4050 4028 l 4049 4011 l 4049 3993 l 4048 3975 l 4046 3957 l 4043 3939 l 4040 3921 l 4035 3904 l 4030 3887 l 4024 3871 l 4017 3855 l 4009 3840 l 4000 3825 l 3991 3812 l 3981 3799 l 3969 3786 l 3957 3772 l 3943 3758 l 3929 3744 l 3914 3730 l 3898 3716 l 3883 3702 l 3867 3689 l 3852 3677 l 3837 3665 l 3824 3654 l 3811 3643 l 3799 3634 l 3788 3625 l 3774 3614 l 3761 3603 l 3749 3593 l 3737 3584 l 3725 3575 l 3714 3566 l 3703 3558 l 3693 3550 l 3682 3543 l 3672 3537 l 3661 3531 l 3650 3525 l 3640 3520 l 3629 3515 l 3616 3510 l 3602 3506 l 3587 3501 l 3570 3498 l 3552 3494 l 3533 3492 l 3512 3491 l 3491 3490 l 3469 3491 l 3447 3493 l 3424 3496 l 3400 3500 l 3382 3504 l 3364 3508 l 3345 3514 l 3325 3520 l 3304 3526 l 3283 3534 l 3261 3543 l 3238 3552 l 3215 3562 l 3193 3573 l 3170 3584 l 3149 3596 l 3128 3608 l 3107 3621 l 3088 3634 l 3071 3647 l 3054 3660 l 3039 3673 l 3025 3686 l cp gs col7 0.90 shd ef gr % Polyline n 300 9600 m 300 9599 l 300 9597 l 300 9592 l 300 9585 l 300 9575 l 300 9561 l 300 9542 l 300 9519 l 300 9491 l 300 9457 l 300 9418 l 300 9373 l 301 9322 l 301 9265 l 301 9202 l 301 9132 l 301 9057 l 302 8976 l 302 8889 l 302 8798 l 302 8701 l 303 8599 l 303 8493 l 303 8383 l 304 8270 l 304 8154 l 305 8035 l 305 7914 l 306 7791 l 306 7667 l 307 7543 l 307 7418 l 308 7292 l 309 7167 l 309 7043 l 310 6920 l 311 6798 l 312 6677 l 312 6558 l 313 6441 l 314 6326 l 315 6214 l 316 6103 l 316 5995 l 317 5890 l 318 5787 l 319 5686 l 320 5588 l 321 5493 l 322 5401 l 324 5311 l 325 5223 l 326 5138 l 327 5056 l 328 4976 l 329 4898 l 331 4822 l 332 4749 l 334 4678 l 335 4609 l 336 4542 l 338 4478 l 340 4414 l 341 4353 l 343 4294 l 345 4236 l 346 4179 l 348 4124 l 350 4071 l 352 4019 l 354 3968 l 356 3918 l 358 3869 l 360 3822 l 363 3775 l 367 3693 l 371 3614 l 376 3537 l 381 3463 l 386 3391 l 391 3321 l 397 3254 l 403 3188 l 409 3125 l 415 3063 l 422 3003 l 429 2946 l 437 2890 l 444 2836 l 452 2784 l 461 2735 l 469 2687 l 478 2641 l 487 2597 l 497 2555 l 507 2515 l 517 2477 l 527 2441 l 537 2407 l 548 2375 l 559 2344 l 570 2316 l 581 2289 l 592 2264 l 604 2240 l 615 2218 l 627 2198 l 639 2179 l 650 2161 l 662 2144 l 675 2128 l 687 2113 l 699 2099 l 712 2086 l 724 2074 l 737 2062 l 750 2050 l 770 2033 l 790 2017 l 812 2001 l 834 1986 l 857 1971 l 880 1957 l 905 1943 l 931 1929 l 957 1916 l 984 1903 l 1012 1891 l 1041 1880 l 1070 1869 l 1100 1858 l 1130 1848 l 1160 1839 l 1190 1831 l 1221 1823 l 1251 1815 l 1281 1809 l 1311 1803 l 1341 1797 l 1370 1792 l 1399 1788 l 1428 1784 l 1456 1781 l 1484 1778 l 1513 1775 l 1543 1773 l 1574 1770 l 1605 1769 l 1636 1767 l 1669 1766 l 1701 1766 l 1734 1766 l 1767 1766 l 1801 1766 l 1835 1767 l 1869 1768 l 1903 1769 l 1936 1771 l 1969 1773 l 2001 1776 l 2033 1778 l 2064 1781 l 2093 1784 l 2122 1787 l 2149 1790 l 2175 1794 l 2200 1797 l 2223 1801 l 2246 1805 l 2267 1809 l 2288 1813 l 2313 1818 l 2336 1823 l 2359 1829 l 2381 1835 l 2402 1842 l 2422 1849 l 2442 1857 l 2460 1865 l 2477 1873 l 2493 1882 l 2509 1891 l 2523 1901 l 2536 1911 l 2548 1921 l 2558 1932 l 2568 1942 l 2577 1953 l 2585 1964 l 2593 1976 l 2600 1988 l 2607 2000 l 2613 2013 l 2619 2027 l 2625 2041 l 2631 2057 l 2637 2074 l 2642 2092 l 2648 2111 l 2653 2131 l 2657 2151 l 2662 2173 l 2666 2195 l 2670 2218 l 2673 2241 l 2676 2265 l 2679 2289 l 2681 2313 l 2684 2337 l 2686 2362 l 2688 2388 l 2689 2409 l 2690 2432 l 2691 2455 l 2692 2479 l 2693 2504 l 2694 2530 l 2694 2557 l 2694 2585 l 2694 2613 l 2693 2642 l 2692 2671 l 2691 2700 l 2690 2729 l 2688 2758 l 2686 2787 l 2683 2815 l 2680 2843 l 2677 2870 l 2674 2896 l 2670 2921 l 2665 2945 l 2661 2968 l 2656 2991 l 2650 3013 l 2643 3038 l 2635 3063 l 2626 3087 l 2617 3111 l 2606 3135 l 2595 3159 l 2583 3182 l 2570 3205 l 2557 3227 l 2543 3249 l 2529 3269 l 2514 3289 l 2500 3308 l 2485 3326 l 2470 3343 l 2456 3359 l 2442 3373 l 2428 3387 l 2414 3400 l 2400 3413 l 2385 3426 l 2369 3438 l 2353 3451 l 2337 3463 l 2320 3476 l 2303 3488 l 2285 3501 l 2267 3514 l 2248 3527 l 2230 3540 l 2211 3553 l 2193 3566 l 2175 3580 l 2157 3593 l 2139 3607 l 2122 3621 l 2105 3635 l 2088 3650 l 2073 3663 l 2059 3676 l 2044 3691 l 2029 3706 l 2014 3722 l 1998 3739 l 1981 3757 l 1965 3776 l 1948 3796 l 1931 3817 l 1914 3839 l 1897 3861 l 1881 3884 l 1864 3907 l 1848 3931 l 1833 3955 l 1818 3979 l 1803 4003 l 1789 4027 l 1776 4051 l 1763 4075 l 1750 4100 l 1740 4121 l 1729 4143 l 1719 4166 l 1709 4189 l 1699 4213 l 1689 4238 l 1678 4264 l 1669 4291 l 1659 4318 l 1649 4347 l 1640 4376 l 1630 4405 l 1621 4435 l 1612 4466 l 1604 4496 l 1596 4527 l 1588 4558 l 1581 4588 l 1574 4619 l 1568 4649 l 1562 4679 l 1556 4709 l 1551 4738 l 1546 4767 l 1542 4796 l 1538 4825 l 1534 4852 l 1531 4880 l 1528 4907 l 1525 4936 l 1522 4965 l 1520 4995 l 1518 5025 l 1517 5056 l 1516 5087 l 1515 5119 l 1515 5152 l 1515 5185 l 1516 5218 l 1517 5252 l 1519 5285 l 1521 5319 l 1524 5352 l 1527 5385 l 1531 5417 l 1535 5449 l 1540 5481 l 1545 5512 l 1551 5542 l 1557 5572 l 1564 5602 l 1571 5631 l 1579 5659 l 1588 5688 l 1596 5716 l 1606 5744 l 1616 5772 l 1627 5801 l 1639 5830 l 1651 5859 l 1665 5889 l 1679 5919 l 1694 5949 l 1709 5979 l 1726 6009 l 1742 6039 l 1760 6069 l 1778 6099 l 1797 6128 l 1816 6157 l 1835 6185 l 1854 6212 l 1874 6239 l 1893 6264 l 1913 6289 l 1933 6313 l 1952 6336 l 1972 6358 l 1991 6379 l 2011 6399 l 2030 6419 l 2050 6438 l 2071 6457 l 2093 6476 l 2115 6494 l 2138 6513 l 2161 6530 l 2184 6548 l 2209 6565 l 2234 6582 l 2259 6598 l 2286 6614 l 2312 6630 l 2339 6645 l 2366 6659 l 2393 6674 l 2420 6687 l 2447 6700 l 2474 6713 l 2501 6724 l 2527 6736 l 2553 6746 l 2578 6756 l 2603 6766 l 2628 6775 l 2652 6784 l 2676 6792 l 2700 6800 l 2722 6807 l 2744 6814 l 2767 6821 l 2790 6828 l 2814 6835 l 2838 6842 l 2863 6848 l 2889 6855 l 2915 6861 l 2943 6867 l 2971 6872 l 3000 6878 l 3030 6883 l 3060 6888 l 3091 6892 l 3123 6896 l 3155 6900 l 3188 6903 l 3221 6906 l 3254 6909 l 3288 6911 l 3322 6912 l 3357 6913 l 3392 6914 l 3427 6914 l 3463 6914 l 3500 6914 l 3538 6913 l 3569 6911 l 3602 6910 l 3635 6908 l 3670 6906 l 3705 6904 l 3741 6901 l 3778 6897 l 3816 6894 l 3855 6890 l 3895 6885 l 3935 6880 l 3976 6875 l 4018 6869 l 4059 6863 l 4101 6856 l 4143 6849 l 4184 6842 l 4226 6834 l 4267 6825 l 4307 6817 l 4346 6808 l 4385 6798 l 4423 6788 l 4459 6778 l 4494 6768 l 4528 6757 l 4561 6747 l 4592 6735 l 4622 6724 l 4650 6712 l 4677 6700 l 4703 6688 l 4727 6675 l 4750 6663 l 4778 6645 l 4804 6627 l 4828 6607 l 4851 6587 l 4872 6566 l 4891 6545 l 4909 6522 l 4926 6498 l 4941 6474 l 4954 6449 l 4967 6424 l 4977 6398 l 4987 6372 l 4995 6345 l 5002 6319 l 5008 6293 l 5013 6267 l 5016 6242 l 5019 6217 l 5021 6193 l 5023 6169 l 5024 6147 l 5025 6125 l 5025 6103 l 5025 6083 l 5025 6063 l 5025 6039 l 5025 6017 l 5025 5994 l 5025 5972 l 5025 5949 l 5024 5927 l 5024 5904 l 5023 5881 l 5022 5859 l 5021 5836 l 5020 5812 l 5018 5789 l 5016 5766 l 5014 5744 l 5012 5721 l 5009 5698 l 5007 5676 l 5003 5653 l 5000 5631 l 4996 5608 l 4992 5586 l 4988 5563 l 4983 5542 l 4979 5522 l 4974 5500 l 4969 5478 l 4964 5455 l 4958 5431 l 4953 5406 l 4947 5381 l 4941 5354 l 4935 5327 l 4928 5300 l 4922 5272 l 4916 5243 l 4910 5214 l 4904 5185 l 4898 5157 l 4893 5128 l 4888 5100 l 4883 5072 l 4879 5044 l 4875 5017 l 4872 4990 l 4869 4964 l 4866 4938 l 4864 4913 l 4863 4888 l 4861 4860 l 4861 4833 l 4861 4806 l 4862 4778 l 4863 4750 l 4866 4721 l 4869 4692 l 4873 4663 l 4878 4634 l 4883 4605 l 4890 4575 l 4898 4546 l 4906 4517 l 4915 4489 l 4925 4461 l 4936 4434 l 4948 4408 l 4961 4383 l 4974 4359 l 4988 4335 l 5002 4313 l 5017 4291 l 5033 4270 l 5050 4250 l 5066 4232 l 5083 4214 l 5102 4196 l 5121 4179 l 5141 4162 l 5162 4145 l 5184 4129 l 5207 4114 l 5231 4099 l 5256 4086 l 5281 4073 l 5307 4061 l 5334 4051 l 5360 4041 l 5387 4033 l 5414 4027 l 5441 4022 l 5468 4019 l 5494 4017 l 5519 4017 l 5545 4018 l 5569 4021 l 5593 4026 l 5617 4032 l 5640 4040 l 5663 4050 l 5682 4060 l 5701 4071 l 5720 4084 l 5739 4098 l 5759 4114 l 5778 4131 l 5797 4150 l 5816 4170 l 5835 4192 l 5854 4216 l 5873 4241 l 5891 4268 l 5909 4296 l 5928 4325 l 5945 4356 l 5962 4387 l 5979 4420 l 5995 4454 l 6011 4488 l 6026 4523 l 6040 4558 l 6054 4594 l 6066 4630 l 6079 4666 l 6090 4702 l 6101 4739 l 6111 4776 l 6120 4813 l 6129 4850 l 6138 4888 l 6144 4921 l 6151 4955 l 6157 4990 l 6163 5025 l 6168 5061 l 6173 5098 l 6178 5136 l 6183 5174 l 6187 5213 l 6191 5253 l 6194 5294 l 6197 5335 l 6200 5376 l 6202 5418 l 6205 5460 l 6206 5502 l 6208 5545 l 6209 5587 l 6209 5629 l 6210 5671 l 6210 5712 l 6210 5752 l 6209 5792 l 6208 5831 l 6207 5870 l 6206 5907 l 6204 5944 l 6202 5980 l 6200 6014 l 6198 6048 l 6196 6081 l 6193 6113 l 6190 6144 l 6188 6175 l 6184 6209 l 6180 6243 l 6176 6276 l 6172 6308 l 6167 6341 l 6162 6373 l 6156 6406 l 6150 6438 l 6144 6470 l 6137 6502 l 6130 6534 l 6122 6566 l 6114 6597 l 6106 6629 l 6097 6659 l 6088 6690 l 6078 6720 l 6068 6750 l 6058 6779 l 6047 6807 l 6036 6835 l 6025 6862 l 6013 6889 l 6001 6915 l 5989 6940 l 5977 6965 l 5965 6990 l 5952 7014 l 5939 7038 l 5925 7063 l 5911 7087 l 5897 7111 l 5882 7135 l 5866 7160 l 5850 7186 l 5833 7211 l 5816 7237 l 5798 7264 l 5780 7291 l 5761 7318 l 5742 7345 l 5722 7373 l 5702 7400 l 5683 7428 l 5662 7456 l 5642 7483 l 5623 7510 l 5603 7537 l 5583 7563 l 5564 7589 l 5545 7614 l 5527 7639 l 5509 7663 l 5492 7686 l 5475 7709 l 5459 7731 l 5443 7752 l 5428 7773 l 5414 7793 l 5400 7813 l 5383 7837 l 5367 7860 l 5351 7884 l 5336 7907 l 5321 7930 l 5306 7954 l 5292 7977 l 5278 8000 l 5264 8023 l 5251 8046 l 5238 8069 l 5226 8091 l 5215 8113 l 5204 8135 l 5193 8157 l 5184 8177 l 5175 8197 l 5166 8217 l 5158 8236 l 5151 8255 l 5144 8273 l 5137 8290 l 5131 8308 l 5125 8325 l 5118 8346 l 5112 8367 l 5106 8388 l 5099 8409 l 5093 8431 l 5088 8454 l 5082 8477 l 5076 8500 l 5071 8523 l 5066 8547 l 5061 8570 l 5056 8592 l 5052 8614 l 5047 8636 l 5043 8657 l 5039 8677 l 5036 8696 l 5032 8715 l 5028 8733 l 5025 8750 l 5021 8771 l 5016 8792 l 5012 8813 l 5007 8835 l 5003 8856 l 4998 8877 l 4994 8898 l 4989 8918 l 4985 8938 l 4981 8957 l 4977 8975 l 4973 8992 l 4970 9008 l 4967 9023 l 4965 9037 l 4963 9050 l 4960 9064 l 4958 9079 l 4957 9093 l 4955 9107 l 4954 9122 l 4954 9137 l 4953 9152 l 4954 9167 l 4954 9183 l 4955 9198 l 4957 9214 l 4958 9230 l 4960 9246 l 4963 9263 l 4965 9278 l 4967 9294 l 4970 9312 l 4973 9330 l 4977 9349 l 4980 9368 l 4984 9388 l 4988 9407 l 4991 9426 l 4995 9445 l 4998 9462 l 5002 9478 l 5005 9492 l 5008 9505 l 5010 9516 l 5013 9525 l 5014 9530 l 5015 9534 l 5015 9538 l 5014 9542 l 5012 9545 l 5009 9548 l 5003 9550 l 4996 9552 l 4985 9553 l 4972 9554 l 4956 9555 l 4937 9555 l 4914 9556 l 4887 9556 l 4857 9555 l 4822 9555 l 4784 9554 l 4741 9554 l 4694 9553 l 4642 9553 l 4587 9552 l 4527 9551 l 4462 9551 l 4392 9550 l 4318 9550 l 4238 9550 l 4191 9550 l 4144 9550 l 4094 9550 l 4043 9550 l 3989 9551 l 3934 9551 l 3878 9551 l 3820 9552 l 3760 9552 l 3699 9553 l 3637 9553 l 3573 9554 l 3508 9555 l 3443 9555 l 3376 9556 l 3309 9557 l 3242 9558 l 3174 9558 l 3106 9559 l 3038 9560 l 2971 9561 l 2904 9562 l 2837 9563 l 2772 9564 l 2707 9565 l 2644 9566 l 2582 9567 l 2522 9568 l 2464 9570 l 2408 9571 l 2354 9572 l 2302 9573 l 2253 9574 l 2206 9575 l 2162 9576 l 2121 9577 l 2083 9578 l 2048 9579 l 2016 9580 l 1987 9581 l 1961 9582 l 1938 9583 l 1919 9584 l 1904 9584 l 1891 9585 l 1882 9586 l 1877 9587 l 1875 9588 l 1876 9588 l 1881 9589 l 1888 9589 l 1898 9590 l 1911 9590 l 1928 9591 l 1947 9591 l 1971 9592 l 1997 9592 l 2028 9593 l 2062 9593 l 2099 9593 l 2141 9594 l 2186 9594 l 2235 9594 l 2289 9595 l 2346 9595 l 2407 9595 l 2473 9596 l 2542 9596 l 2616 9596 l 2694 9596 l 2775 9597 l 2861 9597 l 2950 9597 l 3043 9597 l 3138 9598 l 3237 9598 l 3338 9598 l 3442 9598 l 3547 9598 l 3653 9599 l 3759 9599 l 3865 9599 l 3970 9599 l 4074 9599 l 4174 9599 l 4272 9599 l 4366 9599 l 4454 9600 l 4538 9600 l 4615 9600 l 4686 9600 l 4750 9600 l 4807 9600 l 4856 9600 l 4899 9600 l 4934 9600 l 4962 9600 l 4985 9600 l 5001 9600 l 5012 9600 l 5020 9600 l 5023 9600 l 5025 9600 l gs col7 0.90 shd ef gr % Polyline n 6250 2400 m 6250 2410 l 6252 2420 l 6254 2431 l 6257 2442 l 6261 2453 l 6267 2466 l 6275 2478 l 6283 2492 l 6293 2505 l 6305 2519 l 6317 2533 l 6331 2546 l 6346 2561 l 6363 2575 l 6375 2585 l 6388 2596 l 6403 2608 l 6419 2619 l 6436 2632 l 6454 2644 l 6473 2657 l 6493 2669 l 6515 2682 l 6537 2695 l 6560 2707 l 6584 2719 l 6607 2730 l 6631 2741 l 6655 2751 l 6679 2760 l 6703 2768 l 6727 2775 l 6751 2782 l 6775 2788 l 6799 2792 l 6824 2796 l 6849 2799 l 6875 2801 l 6902 2803 l 6929 2803 l 6957 2802 l 6985 2800 l 7012 2797 l 7040 2793 l 7066 2788 l 7092 2782 l 7117 2775 l 7141 2767 l 7163 2758 l 7183 2748 l 7202 2737 l 7220 2726 l 7236 2713 l 7250 2700 l 7262 2687 l 7273 2673 l 7283 2658 l 7292 2643 l 7300 2626 l 7307 2608 l 7313 2590 l 7318 2570 l 7323 2550 l 7326 2530 l 7327 2509 l 7328 2488 l 7328 2467 l 7327 2446 l 7325 2426 l 7322 2406 l 7318 2386 l 7313 2368 l 7308 2350 l 7302 2332 l 7295 2316 l 7288 2300 l 7278 2283 l 7269 2267 l 7258 2251 l 7246 2235 l 7233 2220 l 7219 2206 l 7204 2191 l 7188 2178 l 7171 2165 l 7154 2153 l 7136 2142 l 7118 2132 l 7100 2123 l 7081 2115 l 7063 2108 l 7045 2102 l 7027 2097 l 7010 2093 l 6992 2090 l 6975 2088 l 6956 2086 l 6936 2086 l 6917 2086 l 6896 2088 l 6876 2090 l 6854 2093 l 6833 2097 l 6811 2102 l 6789 2107 l 6767 2113 l 6746 2119 l 6725 2125 l 6705 2132 l 6685 2138 l 6666 2144 l 6648 2151 l 6630 2157 l 6613 2163 l 6593 2169 l 6574 2175 l 6555 2181 l 6535 2187 l 6515 2193 l 6496 2198 l 6476 2204 l 6457 2209 l 6438 2214 l 6421 2218 l 6404 2223 l 6388 2226 l 6374 2230 l 6361 2233 l 6349 2235 l 6338 2238 l 6317 2241 l 6300 2244 l 6284 2247 l 6271 2248 l 6261 2249 l 6255 2250 l 6251 2250 l 6250 2250 l 6251 2250 l 6252 2250 l 6255 2251 l 6259 2252 l 6263 2253 l 6266 2256 l 6270 2259 l 6273 2264 l 6274 2269 l 6275 2275 l 6274 2283 l 6273 2292 l 6270 2303 l 6266 2315 l 6262 2328 l 6259 2343 l 6255 2357 l 6252 2372 l 6251 2386 l cp gs col7 0.90 shd ef gr % Polyline n 6225 9013 m 6229 8990 l 6234 8968 l 6238 8948 l 6243 8929 l 6248 8910 l 6253 8893 l 6259 8876 l 6264 8860 l 6270 8846 l 6276 8832 l 6282 8819 l 6288 8806 l 6294 8795 l 6300 8784 l 6306 8773 l 6313 8763 l 6320 8750 l 6328 8737 l 6337 8723 l 6346 8709 l 6356 8693 l 6366 8677 l 6377 8661 l 6388 8644 l 6398 8628 l 6409 8611 l 6420 8595 l 6430 8580 l 6440 8565 l 6450 8550 l 6460 8535 l 6470 8520 l 6480 8505 l 6491 8489 l 6502 8473 l 6512 8457 l 6523 8441 l 6534 8425 l 6544 8410 l 6554 8396 l 6563 8383 l 6572 8371 l 6580 8360 l 6588 8350 l 6596 8339 l 6604 8329 l 6613 8319 l 6622 8309 l 6631 8301 l 6641 8293 l 6651 8286 l 6662 8279 l 6674 8274 l 6686 8269 l 6699 8266 l 6713 8263 l 6724 8260 l 6736 8259 l 6749 8257 l 6763 8255 l 6779 8253 l 6795 8250 l 6812 8248 l 6830 8245 l 6849 8241 l 6867 8237 l 6886 8233 l 6904 8228 l 6923 8222 l 6940 8215 l 6958 8208 l 6975 8200 l 6989 8193 l 7003 8185 l 7017 8176 l 7031 8166 l 7045 8155 l 7060 8143 l 7074 8129 l 7088 8115 l 7103 8099 l 7116 8083 l 7130 8065 l 7142 8046 l 7154 8027 l 7165 8007 l 7175 7986 l 7185 7965 l 7193 7944 l 7200 7921 l 7207 7899 l 7213 7875 l 7217 7853 l 7221 7829 l 7224 7805 l 7226 7780 l 7228 7753 l 7229 7726 l 7230 7698 l 7230 7669 l 7230 7640 l 7229 7610 l 7227 7580 l 7225 7551 l 7223 7522 l 7220 7494 l 7217 7466 l 7213 7440 l 7209 7416 l 7205 7392 l 7201 7370 l 7197 7349 l 7192 7330 l 7188 7313 l 7181 7290 l 7174 7269 l 7167 7250 l 7159 7232 l 7151 7216 l 7142 7201 l 7134 7186 l 7125 7173 l 7116 7161 l 7108 7149 l 7099 7138 l 7091 7128 l 7083 7118 l 7076 7108 l 7069 7098 l 7063 7088 l 7056 7076 l 7050 7064 l 7044 7051 l 7039 7037 l 7033 7021 l 7029 7004 l 7025 6987 l 7021 6968 l 7018 6949 l 7017 6929 l 7016 6910 l 7016 6890 l 7017 6870 l 7018 6851 l 7021 6832 l 7025 6813 l 7029 6797 l 7033 6781 l 7038 6765 l 7044 6748 l 7051 6730 l 7059 6712 l 7067 6693 l 7076 6674 l 7086 6654 l 7096 6634 l 7107 6614 l 7118 6593 l 7130 6573 l 7141 6553 l 7153 6533 l 7165 6514 l 7177 6494 l 7189 6475 l 7201 6456 l 7213 6438 l 7224 6420 l 7235 6403 l 7246 6385 l 7258 6367 l 7271 6348 l 7284 6329 l 7297 6309 l 7311 6290 l 7325 6270 l 7339 6250 l 7353 6230 l 7368 6211 l 7383 6192 l 7398 6173 l 7413 6155 l 7427 6138 l 7442 6121 l 7456 6105 l 7470 6090 l 7484 6076 l 7498 6063 l 7513 6050 l 7528 6037 l 7544 6024 l 7560 6011 l 7578 5999 l 7595 5987 l 7614 5976 l 7633 5965 l 7653 5955 l 7673 5945 l 7694 5935 l 7716 5927 l 7737 5918 l 7759 5911 l 7781 5904 l 7803 5898 l 7825 5892 l 7847 5887 l 7868 5883 l 7890 5879 l 7913 5875 l 7933 5872 l 7954 5869 l 7976 5867 l 7998 5864 l 8021 5862 l 8045 5861 l 8069 5859 l 8094 5858 l 8119 5857 l 8145 5856 l 8170 5855 l 8195 5855 l 8219 5855 l 8243 5855 l 8266 5855 l 8288 5856 l 8310 5856 l 8330 5857 l 8349 5858 l 8367 5860 l 8384 5861 l 8400 5863 l 8421 5865 l 8440 5867 l 8459 5871 l 8477 5874 l 8494 5878 l 8511 5883 l 8526 5888 l 8541 5894 l 8556 5901 l 8569 5908 l 8582 5916 l 8594 5924 l 8605 5933 l 8616 5942 l 8627 5952 l 8638 5963 l 8648 5974 l 8660 5986 l 8672 5999 l 8684 6013 l 8697 6028 l 8710 6044 l 8724 6061 l 8738 6078 l 8751 6096 l 8765 6114 l 8778 6131 l 8791 6149 l 8803 6165 l 8815 6182 l 8827 6197 l 8838 6213 l 8850 6230 l 8862 6247 l 8874 6263 l 8886 6280 l 8898 6297 l 8911 6313 l 8923 6329 l 8935 6343 l 8947 6357 l 8959 6368 l 8970 6379 l 8980 6387 l 8990 6394 l 9000 6400 l 9010 6404 l 9020 6407 l 9030 6409 l 9041 6409 l 9052 6408 l 9063 6406 l 9075 6402 l 9087 6397 l 9098 6391 l 9109 6384 l 9120 6377 l 9130 6368 l 9140 6360 l 9150 6350 l 9159 6341 l 9167 6331 l 9176 6321 l 9185 6309 l 9194 6296 l 9202 6282 l 9210 6266 l 9218 6249 l 9225 6230 l 9232 6211 l 9237 6190 l 9242 6169 l 9245 6147 l 9248 6124 l 9249 6100 l 9250 6075 l 9250 6056 l 9249 6036 l 9248 6015 l 9246 5992 l 9243 5969 l 9240 5944 l 9237 5919 l 9233 5893 l 9228 5866 l 9223 5839 l 9218 5811 l 9212 5783 l 9207 5755 l 9201 5728 l 9194 5701 l 9188 5675 l 9182 5650 l 9175 5625 l 9169 5602 l 9163 5580 l 9156 5558 l 9150 5538 l 9144 5517 l 9137 5498 l 9131 5479 l 9124 5459 l 9118 5440 l 9111 5421 l 9104 5401 l 9097 5381 l 9090 5361 l 9082 5340 l 9075 5320 l 9068 5299 l 9060 5278 l 9053 5256 l 9046 5235 l 9039 5213 l 9032 5191 l 9026 5169 l 9019 5146 l 9013 5123 l 9006 5099 l 9000 5075 l 8995 5055 l 8990 5034 l 8985 5013 l 8980 4990 l 8975 4966 l 8970 4942 l 8964 4916 l 8959 4890 l 8953 4863 l 8947 4834 l 8941 4805 l 8935 4776 l 8929 4745 l 8923 4715 l 8917 4684 l 8911 4652 l 8905 4621 l 8898 4590 l 8892 4559 l 8886 4529 l 8880 4498 l 8874 4469 l 8868 4439 l 8862 4411 l 8856 4382 l 8850 4355 l 8844 4327 l 8838 4300 l 8831 4271 l 8824 4242 l 8817 4213 l 8810 4184 l 8802 4154 l 8795 4125 l 8787 4095 l 8779 4065 l 8771 4035 l 8762 4004 l 8753 3975 l 8745 3945 l 8736 3916 l 8727 3887 l 8718 3859 l 8709 3831 l 8700 3805 l 8691 3779 l 8683 3755 l 8674 3732 l 8666 3709 l 8657 3688 l 8649 3668 l 8641 3648 l 8633 3630 l 8625 3613 l 8616 3593 l 8606 3573 l 8597 3555 l 8587 3536 l 8577 3517 l 8566 3498 l 8556 3479 l 8545 3459 l 8534 3439 l 8523 3418 l 8512 3397 l 8502 3375 l 8491 3352 l 8480 3328 l 8469 3303 l 8459 3278 l 8448 3251 l 8438 3224 l 8428 3195 l 8419 3165 l 8409 3133 l 8400 3100 l 8394 3076 l 8387 3051 l 8381 3024 l 8374 2996 l 8367 2967 l 8361 2937 l 8354 2906 l 8347 2873 l 8340 2839 l 8333 2804 l 8326 2768 l 8319 2732 l 8312 2694 l 8305 2655 l 8298 2616 l 8291 2577 l 8284 2538 l 8277 2498 l 8271 2458 l 8264 2419 l 8258 2380 l 8252 2342 l 8246 2304 l 8240 2267 l 8234 2230 l 8229 2195 l 8223 2160 l 8218 2126 l 8214 2094 l 8209 2062 l 8204 2030 l 8200 2000 l 8195 1963 l 8190 1928 l 8185 1892 l 8180 1858 l 8176 1823 l 8171 1789 l 8167 1755 l 8163 1722 l 8159 1689 l 8155 1657 l 8151 1625 l 8148 1594 l 8144 1563 l 8141 1534 l 8139 1505 l 8136 1478 l 8134 1452 l 8132 1426 l 8130 1402 l 8129 1379 l 8128 1358 l 8127 1337 l 8126 1317 l 8125 1298 l 8125 1280 l 8125 1263 l 8125 1241 l 8126 1219 l 8127 1198 l 8128 1177 l 8130 1156 l 8132 1136 l 8134 1115 l 8137 1094 l 8141 1074 l 8144 1053 l 8149 1033 l 8153 1013 l 8158 994 l 8163 974 l 8169 955 l 8175 937 l 8181 918 l 8187 900 l 8193 881 l 8200 863 l 8207 843 l 8215 824 l 8223 803 l 8231 782 l 8240 760 l 8250 738 l 8260 715 l 8271 692 l 8283 669 l 8294 646 l 8307 624 l 8319 602 l 8332 582 l 8345 562 l 8358 544 l 8371 528 l 8385 512 l 8398 498 l 8411 486 l 8425 475 l 8441 464 l 8457 455 l 8473 448 l 8491 441 l 8509 436 l 8528 433 l 8547 431 l 8566 431 l 8586 432 l 8605 434 l 8624 437 l 8643 442 l 8661 448 l 8678 454 l 8694 462 l 8709 470 l 8724 478 l 8738 488 l 8751 497 l 8763 508 l 8775 520 l 8787 533 l 8799 547 l 8810 562 l 8821 579 l 8831 596 l 8841 616 l 8851 636 l 8859 657 l 8867 679 l 8874 702 l 8881 725 l 8886 749 l 8891 774 l 8896 799 l 8900 825 l 8903 845 l 8905 867 l 8908 889 l 8910 912 l 8912 936 l 8914 961 l 8916 987 l 8917 1013 l 8919 1041 l 8921 1068 l 8922 1097 l 8923 1125 l 8925 1153 l 8926 1182 l 8927 1209 l 8928 1237 l 8929 1263 l 8930 1289 l 8931 1314 l 8932 1338 l 8934 1361 l 8935 1383 l 8936 1405 l 8938 1425 l 8939 1449 l 8941 1472 l 8943 1494 l 8946 1516 l 8948 1538 l 8951 1559 l 8954 1581 l 8957 1602 l 8961 1623 l 8964 1643 l 8968 1663 l 8971 1683 l 8975 1702 l 8979 1721 l 8982 1739 l 8986 1757 l 8990 1774 l 8993 1791 l 8997 1808 l 9000 1825 l 9003 1842 l 9007 1860 l 9011 1879 l 9015 1898 l 9019 1918 l 9023 1939 l 9028 1960 l 9033 1982 l 9039 2004 l 9044 2027 l 9051 2049 l 9057 2072 l 9065 2094 l 9072 2116 l 9080 2138 l 9088 2159 l 9097 2179 l 9106 2199 l 9115 2218 l 9125 2238 l 9136 2256 l 9147 2275 l 9159 2294 l 9172 2313 l 9186 2332 l 9201 2351 l 9216 2370 l 9232 2389 l 9248 2407 l 9264 2425 l 9281 2443 l 9297 2459 l 9314 2474 l 9329 2489 l 9345 2502 l 9360 2514 l 9374 2525 l 9387 2534 l 9400 2543 l 9413 2550 l 9432 2560 l 9451 2568 l 9469 2574 l 9486 2578 l 9503 2581 l 9520 2582 l 9535 2583 l 9550 2583 l 9564 2584 l 9576 2584 l 9588 2585 l 9600 2588 l 9610 2590 l 9620 2595 l 9630 2600 l 9640 2606 l 9650 2614 l 9660 2622 l 9670 2632 l 9679 2642 l 9687 2653 l 9694 2665 l 9700 2677 l 9705 2688 l 9710 2700 l 9713 2713 l 9714 2725 l 9715 2738 l 9715 2752 l 9714 2767 l 9711 2782 l 9707 2799 l 9702 2816 l 9696 2833 l 9688 2851 l 9680 2869 l 9670 2886 l 9660 2903 l 9649 2920 l 9638 2938 l 9628 2951 l 9617 2965 l 9606 2979 l 9594 2995 l 9581 3011 l 9568 3027 l 9554 3045 l 9541 3063 l 9527 3082 l 9513 3101 l 9499 3121 l 9486 3141 l 9474 3161 l 9463 3181 l 9452 3201 l 9442 3221 l 9433 3242 l 9425 3263 l 9418 3282 l 9413 3302 l 9407 3322 l 9403 3343 l 9398 3366 l 9395 3388 l 9392 3412 l 9390 3436 l 9389 3460 l 9389 3484 l 9389 3508 l 9390 3532 l 9392 3554 l 9395 3577 l 9398 3598 l 9403 3618 l 9407 3637 l 9413 3655 l 9418 3672 l 9425 3688 l 9433 3704 l 9442 3720 l 9452 3735 l 9463 3750 l 9476 3764 l 9489 3778 l 9504 3791 l 9520 3804 l 9537 3816 l 9555 3828 l 9573 3839 l 9592 3849 l 9612 3859 l 9631 3868 l 9651 3876 l 9671 3884 l 9692 3892 l 9713 3900 l 9732 3907 l 9752 3914 l 9772 3921 l 9793 3929 l 9816 3937 l 9838 3945 l 9862 3954 l 9886 3963 l 9910 3973 l 9934 3984 l 9958 3995 l 9982 4006 l 10004 4018 l 10027 4030 l 10048 4043 l 10068 4056 l 10087 4069 l 10105 4083 l 10122 4097 l 10138 4113 l 10151 4127 l 10164 4142 l 10177 4158 l 10190 4176 l 10202 4194 l 10214 4213 l 10225 4234 l 10237 4255 l 10248 4277 l 10259 4301 l 10270 4325 l 10280 4349 l 10291 4374 l 10301 4399 l 10310 4425 l 10320 4450 l 10329 4475 l 10338 4500 l 10348 4525 l 10357 4550 l 10366 4575 l 10375 4600 l 10384 4623 l 10393 4646 l 10402 4670 l 10412 4695 l 10423 4720 l 10434 4745 l 10446 4771 l 10458 4797 l 10471 4823 l 10485 4850 l 10499 4876 l 10514 4902 l 10529 4928 l 10545 4953 l 10562 4977 l 10578 5001 l 10596 5023 l 10613 5045 l 10631 5065 l 10649 5084 l 10667 5102 l 10686 5119 l 10705 5135 l 10725 5150 l 10745 5164 l 10767 5177 l 10789 5189 l 10812 5201 l 10836 5212 l 10861 5223 l 10887 5233 l 10914 5242 l 10942 5251 l 10970 5259 l 10999 5267 l 11028 5274 l 11058 5280 l 11087 5286 l 11116 5292 l 11145 5297 l 11173 5301 l 11201 5306 l 11227 5309 l 11253 5313 l 11279 5316 l 11303 5319 l 11327 5322 l 11350 5325 l 11377 5328 l 11404 5332 l 11431 5335 l 11457 5339 l 11483 5342 l 11509 5346 l 11534 5349 l 11560 5352 l 11584 5355 l 11608 5357 l 11630 5360 l 11652 5362 l 11672 5363 l 11691 5364 l 11708 5365 l 11724 5366 l 11739 5366 l 11752 5365 l 11764 5364 l 11775 5363 l 11791 5359 l 11805 5354 l 11816 5348 l 11826 5340 l 11835 5332 l 11841 5323 l 11847 5314 l 11851 5305 l 11854 5296 l 11857 5288 l 11860 5281 l 11863 5275 l 11866 5269 l 11871 5263 l 11877 5257 l 11883 5252 l 11891 5245 l 11899 5237 l 11908 5227 l 11918 5216 l 11927 5203 l 11938 5188 l 11944 5176 l 11951 5163 l 11958 5149 l 11966 5133 l 11975 5116 l 11983 5097 l 11992 5078 l 12002 5057 l 12011 5036 l 12021 5015 l 12030 4995 l 12040 4974 l 12049 4955 l 12058 4936 l 12066 4917 l 12075 4900 l 12085 4881 l 12095 4862 l 12105 4843 l 12116 4824 l 12127 4806 l 12137 4788 l 12148 4771 l 12159 4755 l 12169 4740 l 12179 4727 l 12188 4715 l 12197 4705 l 12205 4695 l 12213 4688 l 12216 4684 l 12220 4680 l 12224 4678 l 12228 4676 l 12231 4676 l 12235 4677 l 12239 4679 l 12242 4684 l 12246 4690 l 12249 4700 l 12253 4711 l 12256 4726 l 12259 4744 l 12262 4764 l 12265 4788 l 12268 4816 l 12270 4847 l 12273 4881 l 12275 4919 l 12277 4960 l 12279 5005 l 12281 5053 l 12283 5106 l 12285 5162 l 12286 5222 l 12288 5288 l 12288 5322 l 12289 5357 l 12289 5394 l 12290 5433 l 12291 5472 l 12291 5513 l 12292 5556 l 12292 5600 l 12293 5645 l 12293 5691 l 12293 5739 l 12294 5789 l 12294 5839 l 12295 5891 l 12295 5944 l 12295 5998 l 12296 6054 l 12296 6110 l 12296 6167 l 12297 6226 l 12297 6285 l 12297 6344 l 12298 6405 l 12298 6466 l 12298 6527 l 12298 6588 l 12298 6650 l 12299 6712 l 12299 6774 l 12299 6836 l 12299 6898 l 12299 6959 l 12299 7020 l 12299 7081 l 12300 7141 l 12300 7200 l 12300 7259 l 12300 7317 l 12300 7374 l 12300 7430 l 12300 7485 l 12300 7539 l 12300 7592 l 12300 7645 l 12300 7696 l 12300 7746 l 12300 7795 l 12300 7843 l 12300 7890 l 12300 7936 l 12300 7981 l 12300 8025 l 12300 8087 l 12300 8148 l 12300 8207 l 12300 8264 l 12300 8321 l 12300 8376 l 12300 8430 l 12300 8483 l 12300 8535 l 12300 8586 l 12300 8636 l 12300 8684 l 12300 8732 l 12300 8778 l 12300 8822 l 12300 8866 l 12300 8907 l 12300 8947 l 12300 8986 l 12300 9023 l 12300 9058 l 12300 9092 l 12300 9124 l 12300 9154 l 12300 9183 l 12300 9210 l 12300 9235 l 12300 9259 l 12300 9281 l 12300 9301 l 12300 9321 l 12300 9339 l 12300 9356 l 12300 9371 l 12300 9386 l 12300 9400 l 12300 9418 l 12300 9434 l 12300 9449 l 12300 9463 l 12300 9475 l 12299 9487 l 12299 9497 l 12298 9507 l 12297 9515 l 12296 9522 l 12295 9528 l 12293 9534 l 12291 9538 l 12289 9542 l 12287 9545 l 12284 9547 l 12281 9549 l 12277 9550 l 12274 9551 l 12270 9551 l 12265 9551 l 12260 9551 l 12255 9551 l 12250 9550 l 12244 9550 l 12238 9550 l 12232 9550 l 12227 9550 l 12220 9551 l 12213 9551 l 12205 9551 l 12196 9552 l 12186 9553 l 12174 9553 l 12161 9554 l 12146 9555 l 12129 9556 l 12109 9558 l 12088 9559 l 12065 9560 l 12039 9561 l 12010 9563 l 11979 9564 l 11945 9566 l 11909 9567 l 11870 9569 l 11828 9570 l 11784 9572 l 11736 9573 l 11686 9575 l 11633 9576 l 11578 9578 l 11519 9579 l 11458 9580 l 11394 9582 l 11327 9583 l 11257 9584 l 11183 9585 l 11106 9586 l 11025 9588 l 10979 9588 l 10932 9589 l 10883 9589 l 10833 9590 l 10782 9590 l 10729 9591 l 10675 9591 l 10620 9591 l 10563 9592 l 10505 9592 l 10446 9593 l 10385 9593 l 10323 9593 l 10260 9594 l 10195 9594 l 10130 9595 l 10063 9595 l 9995 9595 l 9927 9595 l 9857 9596 l 9786 9596 l 9715 9596 l 9642 9597 l 9570 9597 l 9496 9597 l 9422 9597 l 9348 9598 l 9273 9598 l 9198 9598 l 9123 9598 l 9048 9598 l 8973 9598 l 8898 9599 l 8823 9599 l 8749 9599 l 8675 9599 l 8602 9599 l 8529 9599 l 8457 9599 l 8386 9599 l 8316 9599 l 8246 9600 l 8178 9600 l 8111 9600 l 8044 9600 l 7979 9600 l 7916 9600 l 7853 9600 l 7792 9600 l 7732 9600 l 7674 9600 l 7617 9600 l 7561 9600 l 7507 9600 l 7454 9600 l 7403 9600 l 7353 9600 l 7305 9600 l 7258 9600 l 7212 9600 l 7168 9600 l 7125 9600 l 7041 9600 l 6962 9600 l 6888 9600 l 6818 9600 l 6753 9600 l 6692 9600 l 6635 9600 l 6582 9600 l 6534 9600 l 6489 9600 l 6447 9600 l 6410 9600 l 6376 9600 l 6346 9600 l 6319 9600 l 6296 9600 l 6276 9600 l 6258 9600 l 6244 9600 l 6232 9600 l 6223 9600 l 6215 9600 l 6210 9600 l 6206 9600 l 6203 9600 l 6201 9600 l 6200 9600 l 6198 9599 l 6196 9598 l 6194 9595 l 6191 9591 l 6187 9584 l 6184 9575 l 6181 9564 l 6179 9549 l 6177 9532 l 6175 9511 l 6175 9488 l 6175 9471 l 6176 9453 l 6176 9434 l 6178 9413 l 6179 9390 l 6181 9366 l 6183 9341 l 6185 9314 l 6188 9287 l 6191 9259 l 6194 9231 l 6197 9203 l 6201 9176 l 6204 9149 l 6208 9123 l 6211 9098 l 6215 9075 l 6218 9053 l 6222 9032 l cp gs col7 0.90 shd ef gr % Polyline n 10950 2100 m 10959 2115 l 10968 2128 l 10977 2139 l 10986 2148 l 10994 2156 l 11002 2164 l 11009 2171 l 11017 2176 l 11022 2179 l 11025 2175 l 11023 2166 l 11019 2154 l 11013 2140 l 11007 2127 l 11000 2113 l 10994 2100 l 10987 2087 l 10980 2073 l 10973 2060 l 10965 2046 l 10957 2034 l 10950 2025 l 10945 2022 l 10941 2023 l 10939 2026 l 10938 2031 l 10938 2037 l 10938 2044 l 10938 2051 l 10938 2058 l 10939 2067 l 10941 2076 l 10945 2088 l cp gs col7 1.00 shd ef gr % Polyline n 10275 6975 m 10250 7000 l 10228 7025 l 10208 7048 l 10191 7067 l 10177 7083 l 10166 7096 l 10158 7107 l 10150 7117 l 10144 7125 l 10138 7133 l 10131 7143 l 10123 7154 l 10114 7167 l 10104 7183 l 10092 7202 l 10078 7225 l 10064 7250 l 10050 7275 l 10041 7293 l 10034 7309 l 10028 7324 l 10023 7335 l 10019 7344 l 10015 7352 l 10012 7357 l 10009 7360 l 10006 7362 l 10004 7363 l 10002 7363 l 10000 7362 l 9998 7362 l 9997 7362 l 9997 7363 l 9997 7364 l 9998 7366 l 9999 7370 l 10003 7375 l 10008 7382 l 10015 7391 l 10024 7401 l 10036 7413 l 10050 7425 l 10070 7440 l 10092 7454 l 10113 7466 l 10133 7476 l 10152 7484 l 10168 7491 l 10182 7496 l 10195 7500 l 10207 7503 l 10219 7506 l 10230 7509 l 10243 7512 l 10257 7516 l 10273 7520 l 10291 7526 l 10313 7533 l 10337 7542 l 10365 7552 l 10395 7564 l 10425 7575 l 10457 7587 l 10484 7598 l 10506 7608 l 10522 7617 l 10532 7626 l 10538 7634 l 10540 7642 l 10539 7649 l 10537 7656 l 10536 7663 l 10535 7668 l 10537 7673 l 10543 7677 l 10553 7678 l 10569 7677 l 10591 7673 l 10618 7664 l 10650 7650 l 10678 7635 l 10705 7617 l 10730 7599 l 10754 7581 l 10774 7564 l 10793 7548 l 10808 7533 l 10822 7519 l 10835 7506 l 10846 7494 l 10856 7481 l 10867 7469 l 10877 7456 l 10889 7442 l 10902 7427 l 10916 7410 l 10931 7391 l 10949 7371 l 10967 7348 l 10987 7324 l 11007 7300 l 11025 7275 l 11040 7252 l 11053 7232 l 11062 7215 l 11068 7201 l 11072 7191 l 11073 7183 l 11073 7177 l 11072 7173 l 11069 7171 l 11066 7169 l 11062 7169 l 11059 7168 l 11055 7168 l 11051 7167 l 11047 7165 l 11043 7162 l 11040 7158 l 11037 7153 l 11034 7147 l 11031 7140 l 11028 7132 l 11025 7125 l 11015 7111 l 11007 7108 l 11002 7112 l 11000 7119 l 10997 7126 l 10990 7131 l 10974 7131 l 10950 7125 l 10931 7118 l 10914 7112 l 10900 7108 l 10889 7106 l 10881 7106 l 10875 7106 l 10869 7106 l 10861 7104 l 10850 7099 l 10836 7089 l 10819 7072 l 10800 7050 l 10785 7028 l 10774 7006 l 10769 6986 l 10767 6969 l 10770 6955 l 10775 6942 l 10781 6931 l 10787 6920 l 10791 6908 l 10791 6895 l 10786 6879 l 10774 6861 l 10754 6843 l 10725 6825 l 10699 6814 l 10671 6806 l 10644 6801 l 10619 6798 l 10595 6797 l 10574 6798 l 10555 6800 l 10536 6803 l 10519 6806 l 10501 6810 l 10484 6813 l 10465 6817 l 10446 6819 l 10426 6822 l 10405 6823 l 10384 6824 l 10365 6825 l 10350 6825 l 10338 6825 l 10340 6824 l 10351 6822 l 10368 6819 l 10389 6816 l 10413 6812 l 10436 6809 l 10458 6807 l 10478 6807 l 10493 6809 l 10501 6815 l 10500 6825 l 10493 6835 l 10482 6845 l 10471 6855 l 10459 6862 l 10448 6867 l 10438 6870 l 10428 6873 l 10419 6875 l 10409 6877 l 10398 6881 l 10385 6887 l 10369 6896 l 10350 6908 l 10328 6926 l 10303 6948 l cp gs col7 1.00 shd ef gr % Polyline n 1650 2625 m 1615 2638 l 1581 2653 l 1549 2667 l 1519 2681 l 1493 2694 l 1470 2706 l 1451 2716 l 1435 2726 l 1421 2734 l 1408 2742 l 1398 2749 l 1387 2756 l 1377 2763 l 1367 2771 l 1354 2780 l 1340 2789 l 1324 2800 l 1305 2812 l 1282 2827 l 1256 2843 l 1226 2862 l 1194 2882 l 1160 2903 l 1125 2925 l 1081 2953 l 1043 2978 l 1011 2997 l 987 3011 l 969 3019 l 956 3023 l 947 3023 l 942 3022 l 937 3019 l 934 3016 l 929 3015 l 923 3017 l 915 3022 l 903 3034 l 887 3052 l 868 3078 l 847 3111 l 825 3150 l 809 3185 l 795 3220 l 783 3254 l 772 3285 l 764 3313 l 756 3338 l 750 3361 l 744 3381 l 739 3399 l 735 3415 l 731 3431 l 728 3447 l 725 3463 l 722 3480 l 721 3499 l 719 3520 l 719 3542 l 721 3567 l 724 3594 l 730 3622 l 738 3649 l 750 3675 l 767 3699 l 786 3716 l 805 3729 l 824 3736 l 841 3740 l 857 3740 l 870 3737 l 883 3732 l 895 3726 l 906 3719 l 918 3711 l 931 3704 l 945 3697 l 961 3691 l 981 3685 l 1003 3681 l 1029 3678 l 1059 3676 l 1091 3675 l 1125 3675 l 1166 3675 l 1201 3676 l 1227 3678 l 1246 3681 l 1257 3685 l 1262 3689 l 1263 3695 l 1263 3700 l 1262 3705 l 1264 3709 l 1270 3712 l 1283 3712 l 1304 3709 l 1335 3703 l 1376 3691 l 1425 3675 l 1460 3662 l 1494 3648 l 1527 3634 l 1556 3622 l 1583 3612 l 1606 3603 l 1626 3596 l 1643 3591 l 1658 3588 l 1671 3585 l 1683 3583 l 1694 3581 l 1705 3579 l 1716 3576 l 1729 3571 l 1744 3565 l 1760 3556 l 1780 3543 l 1802 3526 l 1827 3506 l 1855 3480 l 1886 3449 l 1918 3414 l 1950 3375 l 1978 3337 l 2003 3298 l 2026 3261 l 2046 3225 l 2062 3192 l 2076 3162 l 2088 3135 l 2098 3111 l 2106 3090 l 2112 3070 l 2117 3052 l 2121 3035 l 2125 3019 l 2128 3003 l 2132 2986 l 2135 2968 l 2139 2950 l 2143 2929 l 2147 2907 l 2152 2882 l 2156 2855 l 2162 2825 l 2166 2794 l 2171 2762 l 2174 2730 l 2175 2700 l 2174 2671 l 2170 2647 l 2165 2627 l 2158 2613 l 2152 2602 l 2145 2596 l 2138 2592 l 2131 2592 l 2125 2593 l 2119 2597 l 2113 2601 l 2106 2606 l 2100 2612 l 2093 2617 l 2085 2622 l 2076 2627 l 2066 2631 l 2055 2633 l 2042 2635 l 2027 2635 l 2010 2634 l 1992 2631 l 1971 2628 l 1950 2625 l 1917 2621 l 1888 2617 l 1865 2614 l 1847 2610 l 1836 2606 l 1830 2602 l 1827 2598 l 1825 2594 l 1823 2590 l 1819 2587 l 1810 2586 l 1795 2587 l 1772 2590 l 1740 2597 l 1699 2609 l cp gs col7 1.00 shd ef gr % Polyline n 1575 8100 m 1572 8121 l 1572 8139 l 1573 8153 l 1576 8162 l 1580 8169 l 1584 8172 l 1588 8175 l 1592 8178 l 1597 8181 l 1604 8188 l 1612 8197 l 1622 8211 l 1635 8229 l 1650 8250 l 1666 8271 l 1681 8290 l 1692 8305 l 1699 8316 l 1703 8325 l 1705 8332 l 1706 8338 l 1708 8343 l 1711 8349 l 1717 8356 l 1728 8365 l 1746 8376 l 1770 8388 l 1800 8400 l 1829 8408 l 1855 8414 l 1878 8418 l 1896 8420 l 1909 8421 l 1919 8421 l 1926 8420 l 1931 8419 l 1937 8417 l 1945 8416 l 1956 8414 l 1972 8412 l 1994 8410 l 2023 8407 l 2059 8404 l 2100 8400 l 2137 8396 l 2172 8391 l 2201 8387 l 2225 8383 l 2243 8380 l 2255 8378 l 2264 8377 l 2270 8376 l 2275 8375 l 2280 8374 l 2286 8372 l 2296 8370 l 2310 8367 l 2330 8362 l 2357 8356 l 2390 8347 l 2430 8337 l 2475 8325 l 2516 8314 l 2555 8302 l 2590 8292 l 2620 8283 l 2646 8276 l 2666 8270 l 2683 8266 l 2697 8262 l 2708 8259 l 2719 8256 l 2729 8253 l 2740 8250 l 2753 8246 l 2768 8241 l 2786 8234 l 2808 8226 l 2834 8216 l 2863 8204 l 2894 8190 l 2925 8175 l 2960 8157 l 2988 8140 l 3009 8126 l 3024 8116 l 3034 8107 l 3040 8102 l 3043 8097 l 3044 8094 l 3044 8090 l 3045 8086 l 3047 8081 l 3050 8074 l 3055 8064 l 3062 8053 l 3069 8039 l 3075 8025 l 3077 8019 l 3078 8012 l 3079 8007 l 3080 8002 l 3081 7997 l 3081 7993 l 3082 7990 l 3083 7987 l 3084 7984 l 3086 7982 l 3088 7980 l 3089 7979 l 3092 7978 l 3094 7977 l 3096 7976 l 3098 7976 l 3100 7975 l 3102 7975 l 3103 7974 l 3105 7974 l 3105 7973 l 3105 7972 l 3104 7971 l 3103 7970 l 3100 7969 l 3096 7968 l 3090 7966 l 3083 7964 l 3074 7962 l 3063 7960 l 3051 7957 l 3036 7955 l 3019 7952 l 3000 7950 l 2970 7947 l 2939 7945 l 2908 7943 l 2878 7941 l 2849 7940 l 2822 7939 l 2798 7939 l 2776 7938 l 2755 7938 l 2736 7938 l 2718 7938 l 2700 7938 l 2682 7938 l 2664 7938 l 2645 7938 l 2624 7938 l 2602 7939 l 2578 7939 l 2551 7940 l 2522 7941 l 2492 7943 l 2461 7945 l 2430 7947 l 2400 7950 l 2362 7955 l 2335 7961 l 2317 7966 l 2309 7971 l 2308 7976 l 2313 7980 l 2321 7984 l 2331 7988 l 2342 7991 l 2352 7995 l 2359 7999 l 2362 8004 l 2361 8009 l 2355 8014 l 2342 8020 l 2325 8025 l 2303 8030 l 2281 8032 l 2262 8034 l 2246 8034 l 2233 8034 l 2222 8033 l 2212 8031 l 2203 8030 l 2192 8028 l 2179 8027 l 2163 8026 l 2144 8025 l 2122 8025 l 2100 8025 l 2069 8025 l 2055 8026 l 2055 8029 l 2063 8031 l 2070 8034 l 2056 8032 l 2025 8025 l 2003 8019 l 1981 8013 l 1962 8007 l 1946 8001 l 1933 7996 l 1922 7992 l 1912 7987 l 1903 7983 l 1892 7979 l 1879 7974 l 1863 7968 l 1844 7962 l 1822 7956 l 1800 7950 l 1783 7946 l 1769 7943 l 1760 7940 l 1754 7938 l 1752 7936 l 1752 7934 l 1754 7933 l 1756 7931 l 1759 7930 l 1761 7929 l 1762 7929 l 1760 7930 l 1756 7932 l 1749 7936 l 1738 7942 l 1725 7950 l 1709 7962 l 1693 7974 l 1678 7985 l 1666 7994 l 1655 8001 l 1646 8007 l 1637 8013 l 1629 8018 l 1621 8025 l 1612 8034 l 1602 8045 l 1592 8060 l 1582 8079 l cp gs col7 1.00 shd ef gr % Polyline 7.500 slw [60] 0 sd n 300 8400 m 12300 8400 l 12300 9300 l 300 9300 l cp gs col0 s gr [] 0 sd % Polyline gs clippath 5710 8968 m 5668 9010 l 5798 9141 l 5714 9014 l 5841 9098 l cp eoclip n 6600 10500 m 5775 9075 l 5700 9000 l gs col0 s gr gr % arrowhead n 5841 9098 m 5714 9014 l 5798 9141 l 5798 9098 l 5841 9098 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 8592 1040 m 8636 1081 l 8764 948 l 8639 1036 l 8721 906 l cp eoclip n 10275 -675 m 8625 1050 l gs col0 s gr gr % arrowhead n 8721 906 m 8639 1036 l 8764 948 l 8721 949 l 8721 906 l cp gs 0.00 setgray ef gr col0 s % Polyline 0.000 slw n 7800 8775 m 7768 8793 l 7740 8809 l 7717 8822 l 7698 8832 l 7684 8838 l 7672 8841 l 7664 8843 l 7656 8844 l 7649 8845 l 7642 8847 l 7634 8851 l 7624 8858 l 7612 8868 l 7599 8883 l 7586 8903 l 7575 8925 l 7570 8938 l 7567 8952 l 7564 8965 l 7561 8977 l 7558 8989 l 7555 8999 l 7551 9009 l 7547 9017 l 7543 9025 l 7538 9032 l 7534 9039 l 7529 9045 l 7524 9051 l 7519 9056 l 7514 9062 l 7511 9067 l 7508 9073 l 7507 9079 l 7507 9085 l 7509 9092 l 7514 9098 l 7521 9106 l 7532 9113 l 7547 9121 l 7566 9129 l 7589 9137 l 7617 9144 l 7650 9150 l 7684 9154 l 7720 9157 l 7757 9160 l 7793 9161 l 7828 9161 l 7862 9161 l 7893 9160 l 7922 9159 l 7950 9157 l 7975 9155 l 7998 9153 l 8020 9151 l 8041 9149 l 8061 9146 l 8081 9144 l 8101 9141 l 8122 9138 l 8143 9135 l 8166 9132 l 8190 9129 l 8216 9125 l 8245 9121 l 8276 9117 l 8309 9112 l 8346 9107 l 8384 9102 l 8425 9096 l 8467 9089 l 8509 9082 l 8550 9075 l 8607 9064 l 8655 9053 l 8694 9043 l 8724 9034 l 8746 9028 l 8760 9023 l 8769 9019 l 8774 9016 l 8775 9014 l 8775 9012 l 8774 9011 l 8773 9008 l 8774 9005 l 8777 9000 l 8782 8994 l 8791 8985 l 8803 8974 l 8818 8960 l 8834 8943 l 8850 8925 l 8864 8906 l 8874 8888 l 8883 8871 l 8889 8857 l 8894 8844 l 8898 8834 l 8901 8825 l 8903 8818 l 8905 8812 l 8906 8806 l 8907 8801 l 8907 8795 l 8907 8788 l 8905 8780 l 8902 8770 l 8897 8759 l 8890 8746 l 8880 8731 l 8867 8715 l 8850 8700 l 8827 8684 l 8803 8671 l 8779 8661 l 8757 8653 l 8737 8647 l 8719 8643 l 8704 8640 l 8689 8639 l 8675 8637 l 8661 8637 l 8646 8636 l 8629 8635 l 8610 8633 l 8588 8632 l 8563 8630 l 8535 8628 l 8505 8626 l 8475 8625 l 8436 8627 l 8407 8632 l 8391 8638 l 8384 8646 l 8384 8654 l 8388 8663 l 8391 8671 l 8392 8679 l 8388 8687 l 8376 8693 l 8354 8698 l 8325 8700 l 8298 8699 l 8275 8695 l 8256 8689 l 8243 8681 l 8234 8673 l 8229 8665 l 8225 8656 l 8221 8648 l 8215 8640 l 8205 8632 l 8189 8626 l 8166 8623 l 8136 8622 l 8100 8625 l 8071 8630 l 8044 8637 l 8020 8645 l 8000 8652 l 7984 8659 l 7972 8665 l 7963 8671 l 7956 8676 l 7950 8681 l 7944 8687 l 7937 8693 l 7928 8700 l 7916 8708 l 7900 8718 l 7880 8730 l 7856 8743 l 7829 8759 l cp gs col7 1.00 shd ef gr % Polyline 7.500 slw [120] 0 sd n 150 4800 m 12600 4800 l gs col0 s gr [] 0 sd % Polyline gs clippath 8283 8925 m 8229 8898 l 8147 9063 l 8241 8943 l 8200 9090 l cp eoclip n 7500 10425 m 8250 8925 l gs col0 s gr gr % arrowhead n 8200 9090 m 8241 8943 l 8147 9063 l 8187 9050 l 8200 9090 l cp gs 0.00 setgray ef gr col0 s $F2psEnd rs %%EndDocument endTexFig 1802 5311 a FE(bad)25 b(blo)r(c)n(ks)2274 3572 y(bad)h(blo)r(c)n(ks) 1802 4233 y Fh(f)p FC(v)f FE(=)c Fh(\000)p FE(1)p Fh(g)2322 4588 y(f)p FC(v)j FE(=)d(1)p Fh(g)2770 4989 y(B)2822 4954 y Fp(j)2850 4933 y Ff(\000)2820 5009 y Fp(i)2770 3879 y Fh(B)2822 3844 y Fp(j)2850 3823 y Fe(+)2820 3899 y Fp(i)857 4800 y FC(R)916 4765 y Fp(i;)p Fm(+)915 4821 y Fp(N)1008 4752 y Fl(0)857 4092 y FC(R)916 4056 y Fp(i;)p Fl(\000)915 4113 y Fp(N)1009 4044 y Fl(0)1402 5480 y FD(Figure)27 b(5.)39 b FE(Minimal)26 b(sections.)p eop %%Page: 16 16 16 15 bop 118 45 a Fx(16)1460 b(T.)23 b(BODINEA)n(U)218 374 y FA(F)-8 b(or)24 b(an)m(y)f(spins)e(con\014guration)i(suc)m(h)g (that)h Fv(u)1743 330 y Fs(\020)1743 402 y(N)s(;K)1913 374 y FA(b)s(elongs)e(to)2336 306 y Fq(T)2412 332 y Fs(`)2412 401 y(i)p Fx(=1)2561 374 y Fu(V)7 b FA(\()2676 351 y Fq(b)2659 374 y Fv(R)2729 341 y Fs(i)2757 374 y Fv(;)15 b(\016)s FA(v)m(ol)q(\()3010 351 y Fq(b)2992 374 y Fv(R)3062 341 y Fs(i)3091 374 y FA(\)\),)25 b(the)f(n)m(um)m(b)s(er)118 487 y(of)31 b Fn(b)-5 b(ad)31 b FA(b)s(o)m(xes)g(in)e(a)h(minimal)e (section)i(is)g(b)s(ounded)e(b)m(y)685 703 y Fv(n)740 665 y Fx(+)740 730 y Fs(i)819 703 y FA(+)20 b Fv(n)965 665 y Ft(\000)965 730 y Fs(i)1048 703 y Fr(6)25 b Fv(\016)s FA(v)m(ol)q(\()1357 680 y Fq(b)1339 703 y Fv(R)1409 666 y Fs(i)1438 703 y FA(\))1483 642 y(2)p Fv(c)1567 657 y Fs(d)p 1483 682 126 4 v 1497 766 a Fv(\016)s(h)1633 575 y Fq(\022)1711 642 y Fv(N)p 1710 682 84 4 v 1710 766 a(K)1804 575 y Fq(\023)1871 598 y Fs(d)p Ft(\000)p Fx(1)2042 703 y Fr(6)g FA(2)p Fv(c)2222 718 y Fs(d)2263 703 y Fv(\016)s(h)2358 666 y Fs(d)p Ft(\000)p Fx(1)2505 575 y Fq(\022)2582 642 y Fv(N)p 2582 682 V 2582 766 a(K)2676 575 y Fq(\023)2742 598 y Fs(d)p Ft(\000)p Fx(1)2903 703 y Fv(:)118 925 y FA(As)248 857 y Fq(P)344 883 y Fs(`)344 952 y(i)p Fx(=1)477 925 y Fu(j)522 902 y Fq(b)502 925 y Fv(B)576 892 y Fs(i)604 925 y Fu(j)h FA(=)f Fv(`h)841 892 y Fs(d)p Ft(\000)p Fx(1)997 925 y FA(can)i(b)s(e)e(con)m(trolled)g (in)g(terms)g(of)h(the)g(p)s(erimeter)f(of)h Fv(@)2857 892 y Ft(\003)2897 925 y Fv(v)s FA(,)h(the)f(total)h(n)m(um)m(b)s(er) 118 1033 y(of)k Fn(b)-5 b(ad)31 b FA(b)s(o)m(xes)g(is)e(b)s(ounded)f(b) m(y)1211 1153 y Fs(`)1160 1181 y Fq(X)1169 1376 y Fs(i)p Fx(=1)1307 1267 y Fv(n)1362 1229 y Fx(+)1362 1294 y Fs(i)1440 1267 y FA(+)20 b Fv(n)1586 1229 y Ft(\000)1586 1294 y Fs(i)1670 1267 y Fr(6)25 b Fv(\016)19 b(C)7 b FA(\()p Fv(v)s FA(\))2029 1139 y Fq(\022)2107 1205 y Fv(N)p 2107 1246 V 2107 1329 a(K)2200 1139 y Fq(\023)2267 1161 y Fs(d)p Ft(\000)p Fx(1)2428 1267 y Fv(:)976 b FA(\(3.12\))218 1534 y(The)24 b(previous)f(estimate)i(implies)d(that)j(a)g(mesoscopic)g (in)m(terface)g(is)e(mainly)g(lo)s(cated)i(b)s(et)m(w)m(een)g(the)118 1642 y(t)m(w)m(o)38 b(minimal)c(sections)j(and)f(that)i(the)f (\015uctuations)f(of)h(the)g(in)m(terface)g(necessarily)f(in)m(tersect) h(the)118 1750 y Fn(b)-5 b(ad)34 b FA(b)s(o)m(xes.)50 b(Using)32 b(this)g(mesoscopic)i(information,)e(w)m(e)i(are)f(going)h (to)g(deduce)e(the)i(existence)g(of)f(a)118 1858 y(microscopic)27 b(in)m(terface)h(crossing)f Fv(R)1384 1825 y Fs(i)1383 1885 y(N)1477 1858 y FA(in)g(the)g(direction)f(orthogonal)i(to)e Fv(~)-42 b(n)2726 1872 y Fs(i)2753 1858 y FA(.)40 b(Once)27 b(the)h(microscopic)118 1966 y(in)m(terface)41 b(is)e(lo)s(calized,)j (it)e(will)d(b)s(e)j(p)s(ossible)e(to)j(extract)g(the)g(surface)f (tension)f(factor)i(\(see)h(Step)118 2074 y(3\).)56 b(In)35 b(order)f(to)i(ac)m(hiev)m(e)h(the)e(lo)s(calization,)h(the)f(previous) f(pro)s(ofs)g(for)h(Ising)f(mo)s(del)g([B1)q(,)i(CePi1)o(])118 2182 y(used)i(the)h(prop)s(erties)e(of)i(the)g(FK)g(represen)m(tation)g (and)f(of)h(Pisztora's)g(coarse)h(graining)d([Pi)o(].)66 b(In)118 2290 y(the)41 b(lo)m(w)f(temp)s(erature)g(regime,)j(the)d(pro) s(of)g(can)g(b)s(e)g(simpli\014ed)c(thanks)k(to)h(the)g(coarse)g (graining)118 2398 y(in)m(tro)s(duced)f(previously)f(whic)m(h)h(pro)m (vides)g(a)h(direct)g(corresp)s(ondence)g(b)s(et)m(w)m(een)h(the)f (microscopic)118 2506 y(and)30 b(the)g(mesoscopic)h(scales.)218 2613 y(F)-8 b(rom)39 b(the)g(v)m(ery)g(construction)f(of)h(the)f (coarse)i(graining,)f(the)g(+)f(spin)f(surfaces)i(asso)s(ciated)g(to) 118 2721 y(o)m(v)m(erlapping)c(b)s(o)m(xes)g(with)f(lab)s(el)g(1)h(are) h(connected.)56 b(As)35 b(eac)m(h)i(minimal)32 b(section)k(con)m(tains) f(mainly)118 2829 y(+)30 b(go)s(o)s(d)g(or)g Fu(\000)g FA(go)s(o)s(d)g(blo)s(c)m(ks,)g(there)g(exist,)g(in)f(eac)m(h)i (minimal)d(section,)i(surfaces)g(of)g(+)g(and)g Fu(\000)f FA(spins)118 2937 y(whic)m(h)i(almost)h(cross)g Fv(R)970 2904 y Fs(i)969 2964 y(N)1036 2937 y FA(.)45 b(This)30 b(implies)f(that)k(a)f(microscopic)f(in)m(terface)h(is)f(sandwic)m(hed) g(b)s(et)m(w)m(een)118 3045 y(the)j(t)m(w)m(o)h(minimal)30 b(sections)k(and)e(that)j(the)e(large)h(\015uctuations)e(of)i(this)e (in)m(terface)i(can)g(o)s(ccur)f(only)118 3153 y(through)28 b(the)h Fn(b)-5 b(ad)30 b FA(b)s(o)m(xes.)40 b(By)29 b(mo)s(difying)d(the)j(spins)e(con\014gurations)g Fv(\033)32 b FA(on)d(the)g Fn(b)-5 b(ad)29 b FA(b)s(o)m(xes,)h(w)m(e)f(will)118 3261 y(lo)s(calize)h(the)g(in)m(terface)h(b)s(et)m(w)m(een)g(the)g (minimal)c(sections.)218 3369 y(More)g(precisely)-8 b(,)26 b(w)m(e)g(asso)s(ciate)i(to)e(an)m(y)h(con\014guration)e Fv(\033)30 b FA(the)c(con\014guration)31 b(\026)-50 b Fv(\033)29 b FA(with)c(spins)f(equal)118 3477 y(to)k(+)f(\(resp)g Fu(\000)p FA(\))h(on)f(the)h(b)s(oundary)d(of)j(eac)m(h)g Fn(b)-5 b(ad)29 b FA(b)s(o)m(x)e(in)f(the)h(minimal)e(section)j Fu(B)2968 3444 y Fs(i)2965 3509 y(j)2998 3490 y Fm(+)3079 3477 y FA(\(resp)f Fu(B)3367 3444 y Fs(i)3364 3509 y(j)3397 3490 y Fl(\000)3452 3477 y FA(\))h(and)118 3594 y(equal)i(to)h Fv(\033)j FA(otherwise.)40 b(Let)31 b Fu(A)f FA(b)s(e)f(the)i(image)f (of)h(the)g(set)1092 3672 y Fq(\()1165 3827 y Fv(\033)1311 3723 y Fq(\014)1311 3777 y(\014)1311 3832 y(\014)1433 3827 y Fv(u)1485 3783 y Fs(\020)1485 3856 y(N)s(;K)1632 3827 y FA(\()p Fv(\033)s FA(\))26 b Fu(2)1912 3714 y Fs(`)1875 3741 y Fq(\\)1869 3936 y Fs(i)p Fx(=1)2013 3827 y Fu(V)7 b FA(\()2129 3804 y Fq(b)2111 3827 y Fv(R)2181 3790 y Fs(i)2210 3827 y Fv(;)15 b(\016)s FA(v)m(ol)q(\()2463 3804 y Fq(b)2445 3827 y Fv(R)2515 3790 y Fs(i)2543 3827 y FA(\)\))2613 3672 y Fq(\))118 4072 y FA(b)m(y)37 b(this)f(mapping.)60 b(Inequalit)m(y)36 b(\(3.12\))k(implies)34 b(that)k Fv(\033)j FA(and)g(\026)-50 b Fv(\033)41 b FA(di\013er)36 b(on)h(at)h(most)g Fv(\016)s(C)3290 4086 y Fx(1)3330 4072 y FA(\()p Fv(v)s FA(\))p Fv(N)3530 4039 y Fs(d)p Ft(\000)p Fx(1)118 4179 y FA(sites,)30 b(so)h(that)g(the)g(cost)g(of)f(this)g(surgical)f(pro)s (cedure)g(can)i(b)s(e)e(estimated)i(from)f(ab)s(o)m(v)m(e)356 4413 y Fv(\026)411 4375 y Fx(+)411 4442 y Fs(\014)s(;N)556 4258 y Fq( )628 4413 y Fv(u)680 4369 y Fs(\020)680 4442 y(N)s(;K)852 4413 y Fu(2)981 4299 y Fs(`)945 4327 y Fq(\\)938 4522 y Fs(i)p Fx(=1)1083 4413 y Fu(V)7 b FA(\()1199 4390 y Fq(b)1181 4413 y Fv(R)1251 4376 y Fs(i)1279 4413 y Fv(;)15 b(\016)s FA(v)m(ol)r(\()1532 4390 y Fq(b)1515 4413 y Fv(R)1585 4376 y Fs(i)1613 4413 y FA(\)\))1683 4258 y Fq(!)1796 4413 y Fr(6)40 b FA(exp)2061 4339 y Fq(\000)2103 4413 y Fv(o)p FA(\()p Fv(\016)s FA(\))15 b Fv(C)2340 4427 y Fx(2)2381 4413 y FA(\()p Fv(v)s(;)g(\014)5 b FA(\))p Fv(N)2677 4376 y Fs(d)p Ft(\000)p Fx(1)2809 4339 y Fq(\001)2876 4413 y Fv(\026)2931 4375 y Fx(+)2931 4442 y Fs(\014)s(;N)3061 4339 y Fq(\000)3102 4413 y Fu(A)3175 4339 y Fq(\001)3232 4413 y Fv(:)172 b FA(\(3.13\))218 4642 y(The)35 b(upp)s(er)e(b)s(ound)g(tak)m(es)k(in)m(to)f(accoun)m(t)h (the)e(energetic)i(factor)f(necessary)g(to)g(\015ip)e(some)h(spins)118 4749 y(b)m(y)e(force,)h(as)f(w)m(ell)e(as)i(the)g(com)m(binatorial)f (factor)i(whic)m(h)d(stems)i(from)f(the)h(c)m(hoice)g(of)g(the)g (minimal)118 4857 y(sections.)77 b(In)41 b(a)i(giv)m(en)g(b)s(o)m(x,)i (there)e(are)f(less)g(than)g Fv(N)52 b FA(p)s(ossibilities)38 b(to)43 b(lo)s(cate)h(the)e(heigh)m(t)g(of)h(a)118 4965 y(minimal)36 b(section.)65 b(Once)39 b(this)e(heigh)m(t)i(is)e (\014xed,)j(the)f(n)m(um)m(b)s(er)e(of)i(con\014gurations)f(with)f (di\013eren)m(t)118 5073 y(lo)s(cations)30 b(of)g(bad)g(b)s(o)m(xes)h (is)e(b)s(ounded)f(b)m(y)563 5150 y Fq(\022)652 5217 y FA(\()p Fv(hN)r(=K)7 b FA(\))978 5184 y Fs(d)p Ft(\000)p Fx(1)630 5341 y Fv(\016)s FA(\()p Fv(hN)r(=K)g FA(\))999 5315 y Fs(d)p Ft(\000)p Fx(1)1132 5150 y Fq(\023)1224 5279 y Fr(6)40 b FA(exp)1489 5178 y Fq(\020)1544 5279 y FA(\()p Fv(hN)r(=K)7 b FA(\))1870 5241 y Fs(d)p Ft(\000)p Fx(1)2002 5205 y Fq(\000)2044 5279 y Fv(\016)19 b FA(log)d Fv(\016)24 b FA(+)c(\(1)h Fu(\000)f Fv(\016)s FA(\))15 b(log)s(\(1)21 b Fu(\000)f Fv(\016)s FA(\))3064 5205 y Fq(\001)3107 5178 y(\021)3191 5279 y Fv(:)118 5480 y FA(Summing)28 b(o)m(v)m(er)k(all)d(the)i(con\014gurations)e(leads)h (to)h(the)g(upp)s(er)d(b)s(ound)g(\(3.13\))s(.)p eop %%Page: 17 17 17 16 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(17)118 366 y FF(Remark)42 b(3.2.)k Fn(In)39 b(the)h(c)-5 b(ase)39 b(of)g(Kac)g(Ising)g(mo)-5 b(del,)42 b(it)d(is)g(no)g(longer)h(p)-5 b(ossible)40 b(to)g(lo)-5 b(c)g(alize)40 b(a)g(mi-)118 474 y(cr)-5 b(osc)g(opic)36 b(interfac)-5 b(e.)47 b(Ther)-5 b(efor)g(e)36 b(a)e(mor)-5 b(e)36 b(delic)-5 b(ate)35 b(analysis)g(of)g(surfac)-5 b(e)34 b(tension)h(is)f(r)-5 b(e)g(quir)g(e)g(d)36 b(\(se)-5 b(e)118 582 y(Se)g(ction)33 b(4\).)118 889 y(Step)g(3)g(:)42 b(Surfac)-5 b(e)33 b(tension)g(estimates.)p 118 921 1389 4 v 218 997 a FA(As)41 b(a)h(consequence)g(of)g(the)g(previous)e(step,) k(an)m(y)e(spin)e(con\014guration)h(in)f Fu(A)h FA(con)m(tains)h (micro-)118 1105 y(scopic)28 b(con)m(tours)h(whic)m(h)e(cross)i(eac)m (h)g(cub)s(e)f Fv(R)1714 1072 y Fs(i)1713 1132 y(N)1780 1105 y FA(.)40 b(The)28 b(statistical)g(w)m(eigh)m(t)h(of)f(suc)m(h)g (con)m(tours)h(will)d(b)s(e)118 1213 y(estimated)31 b(b)m(y)f(the)h (surface)f(tension)g(factor.)570 1604 y(lim)15 b(sup)607 1682 y Fs(N)7 b Ft(!1)983 1542 y FA(1)p 899 1583 214 4 v 899 1666 a Fv(N)982 1640 y Fs(d)p Ft(\000)p Fx(1)1137 1604 y FA(log)17 b Fv(\026)1325 1565 y Fx(+)1325 1633 y Fs(\014)s(;N)1454 1604 y FA(\()p Fu(A)p FA(\))26 b Fr(6)45 b Fu(\000)1881 1490 y Fs(`)1830 1517 y Fq(X)1839 1713 y Fs(i)p Fx(=1)1977 1480 y Fq(Z)2042 1669 y Fk(b)2027 1686 y Fs(B)2080 1696 y Fp(i)2126 1604 y Fv(\034)2166 1619 y Fs(\014)2213 1604 y FA(\()n Fv(~)-43 b(n)2303 1618 y Fs(i)2331 1604 y FA(\))15 b Fv(d)p Fu(H)2505 1618 y Fs(x)2570 1604 y FA(+)k Fv(C)2725 1618 y Fx(4)2765 1604 y FA(\()p Fv(\014)5 b(;)15 b(v)s FA(\))p Fv(\016)n(:)388 b FA(\(3.14\))118 1904 y(Com)m(bining)39 b(the)i(previous)f(inequalit)m (y)f(with)h(\(3.13\))s(,)k(w)m(e)d(deduce)g(\(3.11\))r(.)73 b(W)-8 b(e)43 b(no)m(w)e(pro)s(ceed)g(in)118 2012 y(deriving)30 b(\(3.14\))r(.)218 2228 y(Let)i Fv(@)435 2195 y Fx(top)541 2228 y Fv(R)611 2195 y Fs(i)610 2255 y(N)709 2228 y FA(and)f Fv(@)940 2195 y Fx(b)r(ot)1049 2228 y Fv(R)1119 2195 y Fs(i)1118 2255 y(N)1216 2228 y FA(b)s(e)g(the)h(t)m(w)m(o)h(faces)g (of)f Fv(R)2069 2195 y Fs(i)2068 2255 y(N)2166 2228 y FA(orthogonal)g(to)h(the)f(v)m(ector)f Fv(~)-43 b(n)3222 2242 y Fs(i)3250 2228 y FA(.)44 b(The)31 b(face)118 2351 y(con)m(tiguous)26 b(to)h Fv(R)743 2307 y Fs(i;)p Fx(+)742 2380 y Fs(N)871 2351 y FA(will)c(b)s(e)i(denoted)h(b)m(y)g Fv(@)1671 2318 y Fx(top)1777 2351 y Fv(R)1847 2318 y Fs(i)1846 2378 y(N)1914 2351 y FA(.)39 b(F)-8 b(or)26 b(an)m(y)h(spins)c(con\014guration)j(in)e Fu(A)p FA(,)j(w)m(e)f (de\014ne)118 2476 y(the)i(set)g(of)g(sites)g Fv(\015)765 2443 y Fs(i;)p Fx(+)895 2476 y FA(as)g(the)g(supp)s(ort)e(of)i(the)g(+) f(crossing)g(surface)h(in)e Fv(R)2664 2432 y Fs(i;)p Fx(+)2663 2505 y Fs(N)2794 2476 y FA(whic)m(h)h(is)f(the)i(closest)h (to)118 2601 y Fv(@)171 2568 y Fx(top)278 2601 y Fv(R)348 2568 y Fs(i)347 2628 y(N)414 2601 y FA(.)39 b(In)25 b(the)h(same)g(w)m (a)m(y)-8 b(,)29 b Fv(\015)1213 2568 y Fs(i;)p Ft(\000)1341 2601 y FA(is)c(the)h(lo)s(cation)f(of)h(the)g(surface)g(of)g Fu(\000)g FA(spins)d(crossing)i Fv(R)3303 2557 y Fs(i;)p Ft(\000)3302 2630 y Fs(N)3432 2601 y FA(whic)m(h)118 2717 y(is)i(the)i(closest)f(to)h Fv(@)810 2684 y Fx(b)r(ot)918 2717 y Fv(R)988 2684 y Fs(i)987 2744 y(N)1055 2717 y FA(.)39 b(Con)m(trary)29 b(to)f(the)h(pro)s(of)e(of)h(the)h(lo)m(w)m (er)f(b)s(ound,)f(the)h(lo)s(calization)f(of)h(the)118 2828 y(in)m(terfaces)h(has)f(b)s(een)g(deduced)g(from)g(the)h Fy(L)1669 2795 y Fx(1)1743 2828 y FA(constrain)m(t.)40 b(As)28 b(a)h(consequence)h(of)e(this,)h(w)m(e)g(ha)m(v)m(e)g(no)118 2936 y(con)m(trol)g(of)g(the)h(con\014gurations)e(outside)g(the)h(sets) g(\()p Fv(R)2013 2903 y Fs(i)2012 2963 y(N)2080 2936 y FA(\))2115 2951 y Fs(i)20 b Fd(6)f Fs(`)2266 2936 y FA(.)40 b(This)27 b(prev)m(en)m(ts)j(us)e(to)i(conclude)e(that)118 3044 y(all)k(the)i(crossing)e(in)m(terfaces)i(merge)g(in)m(to)f(con)m (tours)g(surrounding)d(the)k(connected)g(comp)s(onen)m(ts)f(of)118 3152 y Fv(v)h FA(as)c(it)g(w)m(as)h(the)g(case)g(for)f(the)h(lo)m(w)m (er)f(b)s(ound)f(\(see)i(\014gure)f(6\).)218 3260 y(W)-8 b(e)35 b(\014rst)e(pin)f(the)i(in)m(terfaces)g(on)g(the)g(sides)e(of)i (eac)m(h)h Fv(R)2193 3227 y Fs(i)2192 3287 y(N)2293 3260 y FA(b)m(y)f(imp)s(osing)d(that)k(the)f(spins)d(on)j(the)118 3384 y(b)s(oundary)25 b(of)i(eac)m(h)i Fv(R)896 3339 y Fs(i;)p Fx(+)895 3412 y Fs(N)1025 3384 y FA(\(resp)e Fv(R)1320 3339 y Fs(i;)p Ft(\000)1319 3412 y Fs(N)1422 3384 y FA(\))h(parallel)d(to)g Fv(~)-42 b(n)1968 3398 y Fs(i)2023 3384 y FA(are)27 b(equal)g(to)h(1)f(\(resp)g Fu(\000)p FA(1\).)40 b(Since)26 b(the)h(heigh)m(t)118 3500 y(of)32 b Fv(R)293 3467 y Fs(i)292 3527 y(N)392 3500 y FA(is)f Fv(\016)s(h)p FA(,)j(this)d(pro)s(cedure)g(requires)g (to)i(\015ip)d(at)j(most)g Fv(\016)s(h)2290 3467 y Fs(d)p Ft(\000)p Fx(1)2422 3500 y Fv(N)2505 3467 y Fs(d)p Ft(\000)p Fx(1)2667 3500 y FA(spins.)45 b(Therefore)32 b(this)f(has)118 3607 y(no)25 b(further)g(impact)g(on)g(the)h(ev)-5 b(aluation)25 b(of)g(the)h(statistical)f(w)m(eigh)m(ts)h(of)g(the)g(con\014gurations) e(b)s(ecause)118 3715 y(the)31 b(cost)g(of)g(\015ipping)c(these)k (spins)d(is)h(b)s(ounded)g(b)m(y)h(exp\()p Fv(\016)s(C)7 b FA(\()p Fv(v)s FA(\))15 b Fv(N)2448 3682 y Fs(d)p Ft(\000)p Fx(1)2580 3715 y FA(\).)218 3823 y(Let)32 b Fu(f)p FA(\000)484 3837 y Fs(j)521 3823 y Fu(g)566 3838 y Fs(j)23 b Fd(6)d Fs(k)767 3823 y FA(\(with)31 b Fv(k)g Fr(6)d Fv(`)p FA(\))k(b)s(e)f (the)i(collection)e(of)h(the)g(con)m(tours)h(obtained)e(b)m(y)h (extending)f(the)118 3936 y(microscopic)c(in)m(terfaces)g(outside)g (eac)m(h)h Fv(R)1589 3903 y Fs(i)1588 3963 y(N)1683 3936 y FA(\(see)g(\014gure)e(6\).)41 b(T)-8 b(o)27 b(eac)m(h)i(\000)2646 3950 y Fs(j)2682 3936 y FA(,)f(w)m(e)g(asso)s(ciate)g(t)m(w)m(o)h(sets) e(of)118 4050 y(sites)g(\(\000)410 4012 y Fx(+)410 4077 y Fs(j)469 4050 y Fv(;)15 b FA(\000)566 4012 y Ft(\000)566 4077 y Fs(j)626 4050 y FA(\))28 b(de\014ned)e(as)i(follo)m(ws)e(:)39 b(If)27 b(\000)1612 4064 y Fs(j)1676 4050 y FA(crosses)h(the)g(set)g Fv(R)2336 4017 y Fs(i)2335 4077 y(N)2429 4050 y FA(then)g(the)f (restriction)g(of)g(\000)3377 4012 y Fx(+)3377 4077 y Fs(j)3464 4050 y FA(\(resp)118 4177 y(\000)175 4139 y Ft(\000)175 4204 y Fs(j)234 4177 y FA(\))35 b(inside)e Fv(R)637 4144 y Fs(i)636 4204 y(N)738 4177 y FA(coincide)h(with)g Fv(\015)1355 4144 y Fs(i;)p Fx(+)1493 4177 y FA(\(resp)g Fv(\015)1777 4144 y Fs(i;)p Ft(\000)1880 4177 y FA(\).)55 b(Outside)34 b Fu([)2400 4144 y Fs(`)2400 4203 y(i)p Fx(=1)2518 4177 y Fv(R)2588 4144 y Fs(i)2587 4204 y(N)2654 4177 y FA(,)i(the)g(sets)f(\000)3116 4139 y Ft(\006)3116 4204 y Fs(j)3210 4177 y FA(con)m(tain)g(the)118 4304 y(sites)26 b(whic)m(h)f(supp)s(ort)g(the)i Fu(\006)f FA(spins)e(of)i(the)h(con)m(tour)g(\000)2016 4318 y Fs(j)2052 4304 y FA(.)40 b(Th)m(us)25 b(\(\000)2435 4266 y Fx(+)2435 4331 y Fs(j)2494 4304 y Fv(;)15 b FA(\000)2591 4266 y Ft(\000)2591 4331 y Fs(j)2651 4304 y FA(\))26 b(should)f(b)s(e)g(in)m (terpreted)h(as)118 4429 y(a)33 b(mo)s(di\014ed)e(\\con)m(tour")j (in\015ated)e(in)f(the)i(regions)f Fv(R)1973 4396 y Fs(i)1972 4456 y(N)2039 4429 y FA(.)48 b(Let)33 b(\001)2353 4396 y Fs(i)2353 4456 y(N)2453 4429 y FA(b)s(e)f(the)h(domain)e(in)h Fv(R)3242 4396 y Fs(i)3241 4456 y(N)3341 4429 y FA(b)s(et)m(w)m(een)118 4541 y Fv(\015)170 4508 y Fs(i;)p Fx(+)273 4541 y Fv(;)15 b(\015)365 4508 y Fs(i;)p Ft(\000)468 4541 y FA(.)218 4861 y(F)-8 b(or)36 b(simplicit)m(y)-8 b(,)35 b(w)m(e)g(\014rst)g (consider)f(the)i(case)g(of)g(a)g(single)e(con)m(tour)i(\000)2715 4875 y Fx(1)2754 4861 y FA(.)56 b(W)-8 b(e)37 b(supp)s(ose)d(that)i (\000)3603 4823 y Fx(+)3603 4887 y(1)118 4974 y FA(surrounds)26 b(\000)594 4935 y Ft(\000)594 5000 y Fx(1)681 4974 y FA(and)i(denote)i(b)m(y)e(ext)q(\(\000)1488 4935 y Fx(+)1488 5000 y(1)1547 4974 y FA(\))h(the)g(exterior)f(of)h(\000)2259 4935 y Fx(+)2259 5000 y(1)2346 4974 y FA(and)f(b)m(y)h(in)m(t)o(\(\000) 2846 4935 y Ft(\000)2846 5000 y Fx(1)2906 4974 y FA(\))g(the)f(in)m (terior)g(of)h(\000)3603 4935 y Ft(\000)3603 5000 y Fx(1)118 5086 y FA(\(see)i(\014gure)f(6\).)42 b(In)29 b(this)h(w)m(a)m(y)-8 b(,)32 b(the)e(domain)f Fy(D)1732 5100 y Fs(N)1836 5086 y FA(is)g(partionned)g(b)m(y)h(\(\000)2605 5048 y Fx(+)2605 5112 y(1)2664 5086 y Fv(;)15 b FA(\000)2761 5048 y Ft(\000)2761 5112 y Fx(1)2821 5086 y FA(\))30 b(in)m(to)1147 5395 y Fy(D)1207 5409 y Fs(N)1306 5395 y FA(=)24 b(ext)q(\(\000)1617 5357 y Fx(+)1617 5421 y(1)1676 5395 y FA(\))1726 5309 y Fq(_)1843 5395 y FA(in)m(t\(\000)2044 5357 y Ft(\000)2044 5421 y Fx(1)2103 5395 y FA(\))2196 5282 y Fs(`)2160 5309 y Fq(_)2153 5504 y Fs(i)p Fx(=1)2283 5395 y FA(\001)2359 5358 y Fs(i)2359 5418 y(N)2441 5395 y Fv(:)p eop %%Page: 18 18 18 17 bop 118 45 a Fx(18)1460 b(T.)23 b(BODINEA)n(U)473 283 y 22599916 11188078 0 0 69070848 34074951 startTexFig 473 283 a %%BeginDocument: ./pictures/contours.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: contours.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Tue Nov 28 17:16:09 2000 %%For: bodineau@gauss.math.jussieu.fr (Thierry Bodineau,56/66-510,73773,,CR) %%BoundingBox: 0 0 1050 518 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 518 moveto 0 0 lineto 1050 0 lineto 1050 518 lineto closepath clip newpath % Fill background color 0 0 moveto 1050 0 lineto 1050 518 lineto 0 518 lineto closepath 1.00 1.00 1.00 setrgbcolor fill 67.0 569.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline 7.500 slw [15 45] 45 sd n -915 7925 m -914 7912 l -914 7897 l -913 7882 l -912 7865 l -911 7848 l -910 7829 l -909 7809 l -908 7788 l -907 7766 l -906 7743 l -905 7720 l -904 7696 l -902 7671 l -901 7647 l -899 7622 l -897 7598 l -896 7573 l -894 7549 l -892 7525 l -890 7500 l -888 7479 l -886 7458 l -884 7436 l -882 7414 l -880 7391 l -878 7367 l -875 7342 l -873 7317 l -870 7291 l -867 7265 l -864 7238 l -861 7210 l -859 7183 l -856 7156 l -853 7128 l -850 7101 l -847 7074 l -844 7048 l -841 7022 l -838 6996 l -835 6971 l -833 6946 l -830 6922 l -828 6898 l -825 6875 l -823 6852 l -820 6829 l -818 6806 l -815 6781 l -813 6757 l -810 6731 l -807 6705 l -804 6678 l -800 6650 l -797 6622 l -793 6593 l -789 6563 l -785 6533 l -781 6503 l -776 6472 l -772 6441 l -767 6410 l -762 6379 l -756 6347 l -751 6316 l -745 6284 l -739 6252 l -733 6220 l -727 6188 l -720 6155 l -714 6128 l -708 6100 l -702 6071 l -696 6042 l -689 6012 l -682 5981 l -674 5949 l -666 5916 l -658 5883 l -650 5849 l -641 5815 l -632 5780 l -623 5745 l -614 5709 l -604 5673 l -594 5637 l -585 5602 l -575 5566 l -565 5531 l -555 5497 l -545 5463 l -535 5429 l -525 5397 l -515 5365 l -505 5334 l -496 5304 l -486 5276 l -477 5248 l -467 5221 l -458 5195 l -449 5169 l -440 5145 l -427 5111 l -414 5078 l -400 5045 l -387 5014 l -373 4984 l -360 4954 l -346 4925 l -332 4897 l -318 4870 l -304 4845 l -290 4820 l -277 4797 l -264 4775 l -251 4754 l -238 4735 l -227 4717 l -215 4701 l -205 4686 l -195 4672 l -185 4660 l -176 4648 l -168 4638 l -155 4622 l -142 4608 l -130 4595 l -119 4583 l -107 4572 l -96 4562 l -85 4554 l -74 4546 l -64 4539 l -54 4533 l -44 4528 l -34 4523 l -25 4519 l -15 4515 l -5 4511 l 6 4507 l 17 4503 l 30 4499 l 43 4494 l 57 4490 l 71 4486 l 86 4481 l 102 4477 l 117 4473 l 132 4470 l 147 4466 l 162 4463 l 178 4460 l 193 4457 l 209 4454 l 226 4452 l 243 4449 l 262 4446 l 281 4444 l 300 4441 l 319 4439 l 337 4437 l 356 4435 l 373 4434 l 389 4432 l 405 4431 l 420 4430 l 435 4429 l 449 4428 l 464 4428 l 479 4427 l 494 4426 l 510 4426 l 526 4425 l 543 4424 l 559 4424 l 575 4423 l 591 4422 l 607 4422 l 624 4421 l 640 4420 l 653 4419 l 667 4418 l 682 4417 l 697 4416 l 714 4415 l 731 4414 l 749 4413 l 768 4412 l 788 4410 l 808 4409 l 829 4408 l 850 4407 l 871 4406 l 892 4405 l 913 4404 l 935 4404 l 956 4403 l 978 4403 l 996 4402 l 1014 4402 l 1033 4402 l 1053 4402 l 1074 4402 l 1095 4402 l 1118 4402 l 1141 4402 l 1164 4403 l 1189 4403 l 1213 4404 l 1238 4404 l 1263 4405 l 1288 4405 l 1313 4406 l 1338 4406 l 1363 4407 l 1387 4407 l 1410 4408 l 1434 4409 l 1457 4409 l 1480 4410 l 1503 4411 l 1527 4411 l 1551 4412 l 1575 4413 l 1600 4413 l 1626 4414 l 1652 4415 l 1679 4416 l 1706 4417 l 1733 4418 l 1761 4419 l 1788 4420 l 1815 4421 l 1842 4422 l 1868 4423 l 1894 4424 l 1918 4425 l 1943 4427 l 1966 4428 l 1989 4430 l 2011 4431 l 2033 4433 l 2056 4434 l 2080 4436 l 2103 4438 l 2127 4440 l 2152 4443 l 2176 4445 l 2201 4448 l 2226 4451 l 2251 4454 l 2276 4457 l 2301 4460 l 2325 4464 l 2349 4467 l 2373 4471 l 2395 4474 l 2418 4478 l 2439 4481 l 2460 4485 l 2480 4489 l 2500 4493 l 2520 4496 l 2540 4500 l 2560 4504 l 2581 4509 l 2602 4513 l 2623 4518 l 2645 4523 l 2667 4528 l 2688 4532 l 2710 4538 l 2731 4543 l 2752 4547 l 2772 4552 l 2792 4557 l 2810 4562 l 2828 4566 l 2846 4571 l 2862 4575 l 2877 4579 l 2893 4583 l 2909 4587 l 2925 4591 l 2941 4595 l 2957 4599 l 2974 4603 l 2991 4607 l 3009 4610 l 3028 4614 l 3047 4618 l 3067 4621 l 3088 4624 l 3109 4627 l 3131 4630 l 3154 4632 l 3177 4635 l 3201 4637 l 3226 4638 l 3253 4640 l 3272 4641 l 3292 4642 l 3313 4643 l 3335 4644 l 3359 4644 l 3384 4645 l 3410 4645 l 3437 4646 l 3465 4646 l 3495 4646 l 3526 4646 l 3557 4646 l 3589 4646 l 3622 4646 l 3656 4645 l 3690 4645 l 3724 4644 l 3758 4643 l 3792 4642 l 3826 4641 l 3860 4640 l 3894 4639 l 3927 4637 l 3961 4636 l 3994 4634 l 4028 4633 l 4057 4631 l 4086 4629 l 4116 4627 l 4147 4625 l 4178 4623 l 4210 4621 l 4242 4618 l 4275 4616 l 4308 4613 l 4342 4610 l 4376 4607 l 4410 4604 l 4445 4601 l 4480 4598 l 4514 4594 l 4549 4591 l 4583 4587 l 4616 4584 l 4649 4580 l 4681 4577 l 4713 4573 l 4744 4569 l 4773 4566 l 4802 4562 l 4830 4558 l 4857 4555 l 4884 4551 l 4909 4547 l 4934 4544 l 4958 4540 l 4989 4535 l 5020 4530 l 5050 4525 l 5080 4519 l 5110 4514 l 5139 4508 l 5168 4502 l 5196 4497 l 5224 4491 l 5251 4485 l 5278 4479 l 5304 4474 l 5329 4468 l 5353 4463 l 5376 4457 l 5398 4452 l 5418 4448 l 5438 4443 l 5457 4439 l 5475 4435 l 5493 4431 l 5510 4428 l 5527 4424 l 5544 4421 l 5561 4418 l 5578 4415 l 5596 4412 l 5614 4410 l 5634 4407 l 5654 4405 l 5676 4402 l 5698 4400 l 5721 4398 l 5745 4397 l 5771 4395 l 5797 4394 l 5824 4392 l 5852 4391 l 5881 4390 l 5911 4390 l 5942 4389 l 5974 4388 l 6007 4388 l 6043 4388 l 6066 4387 l 6091 4387 l 6116 4387 l 6143 4387 l 6171 4387 l 6199 4387 l 6229 4387 l 6260 4387 l 6293 4388 l 6326 4388 l 6360 4389 l 6396 4389 l 6432 4390 l 6469 4391 l 6507 4392 l 6546 4393 l 6585 4394 l 6625 4395 l 6665 4396 l 6705 4398 l 6746 4400 l 6786 4401 l 6826 4403 l 6866 4405 l 6906 4407 l 6946 4410 l 6985 4412 l 7023 4415 l 7062 4417 l 7099 4420 l 7137 4423 l 7174 4426 l 7211 4429 l 7248 4433 l 7282 4436 l 7317 4439 l 7351 4443 l 7387 4447 l 7422 4451 l 7458 4455 l 7494 4459 l 7530 4464 l 7567 4468 l 7604 4473 l 7642 4478 l 7680 4483 l 7719 4488 l 7757 4493 l 7796 4498 l 7835 4503 l 7874 4508 l 7912 4514 l 7951 4519 l 7990 4524 l 8028 4529 l 8066 4534 l 8103 4539 l 8140 4544 l 8176 4548 l 8212 4553 l 8247 4557 l 8282 4561 l 8316 4565 l 8349 4569 l 8381 4573 l 8414 4576 l 8445 4579 l 8476 4582 l 8507 4585 l 8538 4588 l 8572 4590 l 8606 4593 l 8640 4595 l 8674 4597 l 8708 4599 l 8743 4600 l 8777 4602 l 8812 4603 l 8848 4604 l 8883 4605 l 8918 4606 l 8954 4606 l 8990 4607 l 9025 4607 l 9060 4608 l 9095 4608 l 9130 4608 l 9164 4608 l 9197 4607 l 9230 4607 l 9262 4607 l 9294 4606 l 9324 4606 l 9354 4606 l 9383 4605 l 9411 4605 l 9438 4604 l 9464 4604 l 9490 4603 l 9515 4603 l 9539 4603 l 9563 4603 l 9593 4602 l 9624 4602 l 9654 4602 l 9684 4602 l 9713 4602 l 9743 4602 l 9772 4603 l 9801 4603 l 9830 4603 l 9859 4603 l 9887 4603 l 9915 4603 l 9942 4603 l 9968 4603 l 9994 4603 l 10019 4603 l 10043 4602 l 10066 4602 l 10088 4601 l 10109 4600 l 10130 4599 l 10150 4598 l 10169 4597 l 10188 4595 l 10210 4593 l 10232 4590 l 10254 4587 l 10276 4584 l 10298 4580 l 10321 4576 l 10344 4572 l 10366 4567 l 10389 4563 l 10412 4558 l 10434 4552 l 10455 4547 l 10476 4542 l 10497 4537 l 10517 4531 l 10536 4526 l 10554 4521 l 10571 4517 l 10588 4512 l 10605 4508 l 10623 4503 l 10642 4498 l 10660 4493 l 10679 4488 l 10698 4484 l 10718 4480 l 10738 4475 l 10758 4472 l 10778 4468 l 10799 4465 l 10819 4462 l 10839 4460 l 10859 4458 l 10879 4457 l 10898 4456 l 10917 4456 l 10936 4457 l 10955 4458 l 10971 4459 l 10987 4460 l 11004 4462 l 11021 4464 l 11040 4466 l 11059 4469 l 11079 4472 l 11101 4475 l 11123 4479 l 11147 4482 l 11171 4486 l 11196 4490 l 11222 4493 l 11249 4497 l 11276 4501 l 11304 4504 l 11332 4507 l 11361 4510 l 11390 4513 l 11420 4516 l 11451 4518 l 11483 4520 l 11508 4521 l 11535 4523 l 11562 4524 l 11591 4525 l 11620 4525 l 11651 4526 l 11682 4526 l 11714 4527 l 11747 4527 l 11781 4527 l 11815 4526 l 11850 4526 l 11885 4526 l 11919 4525 l 11954 4524 l 11988 4523 l 12022 4522 l 12055 4521 l 12088 4519 l 12119 4518 l 12149 4516 l 12178 4514 l 12206 4513 l 12233 4511 l 12258 4509 l 12283 4507 l 12306 4505 l 12328 4503 l 12360 4499 l 12390 4495 l 12418 4491 l 12445 4487 l 12471 4483 l 12495 4478 l 12518 4473 l 12540 4469 l 12561 4464 l 12580 4459 l 12599 4455 l 12616 4451 l 12633 4447 l 12649 4443 l 12664 4440 l 12678 4437 l 12693 4435 l 12708 4433 l 12721 4431 l 12735 4430 l 12750 4429 l 12766 4428 l 12783 4427 l 12801 4427 l 12820 4427 l 12839 4428 l 12860 4429 l 12881 4430 l 12903 4431 l 12925 4432 l 12947 4434 l 12970 4436 l 12993 4438 l 13016 4440 l 13039 4442 l 13063 4445 l 13086 4447 l 13110 4450 l 13132 4453 l 13155 4455 l 13179 4458 l 13203 4461 l 13228 4464 l 13254 4468 l 13281 4471 l 13308 4475 l 13336 4479 l 13364 4483 l 13393 4487 l 13421 4491 l 13449 4496 l 13476 4500 l 13502 4504 l 13528 4509 l 13553 4513 l 13577 4518 l 13600 4522 l 13622 4526 l 13642 4531 l 13663 4535 l 13686 4540 l 13709 4546 l 13731 4552 l 13754 4558 l 13775 4564 l 13797 4570 l 13818 4577 l 13839 4584 l 13859 4590 l 13879 4597 l 13898 4604 l 13916 4611 l 13934 4617 l 13951 4624 l 13967 4630 l 13982 4636 l 13998 4642 l 14013 4648 l 14029 4654 l 14046 4660 l 14064 4667 l 14082 4674 l 14101 4680 l 14120 4687 l 14140 4694 l 14160 4701 l 14179 4708 l 14199 4714 l 14218 4721 l 14237 4727 l 14254 4732 l 14272 4738 l 14289 4743 l 14305 4748 l 14321 4752 l 14338 4757 l 14355 4761 l 14372 4766 l 14390 4770 l 14408 4775 l 14426 4780 l 14445 4784 l 14463 4789 l 14481 4793 l 14499 4798 l 14517 4802 l 14534 4806 l 14550 4810 l 14567 4814 l 14583 4818 l 14598 4821 l 14615 4825 l 14631 4830 l 14649 4834 l 14666 4838 l 14685 4843 l 14703 4848 l 14722 4853 l 14740 4858 l 14759 4863 l 14777 4867 l 14794 4872 l 14811 4877 l 14827 4881 l 14842 4886 l 14858 4890 l 14875 4895 l 14892 4900 l 14910 4905 l 14928 4911 l 14946 4916 l 14964 4922 l 14983 4929 l 15001 4935 l 15019 4941 l 15036 4947 l 15053 4954 l 15068 4960 l 15083 4966 l 15098 4973 l 15112 4979 l 15126 4986 l 15140 4993 l 15155 5001 l 15170 5009 l 15185 5017 l 15200 5026 l 15215 5034 l 15229 5043 l 15243 5051 l 15255 5060 l 15268 5067 l 15279 5075 l 15290 5083 l 15302 5091 l 15315 5100 l 15327 5109 l 15340 5119 l 15353 5129 l 15366 5139 l 15378 5149 l 15390 5160 l 15402 5171 l 15412 5181 l 15423 5192 l 15433 5203 l 15441 5212 l 15449 5222 l 15458 5233 l 15467 5245 l 15476 5257 l 15485 5270 l 15494 5284 l 15503 5299 l 15512 5313 l 15521 5328 l 15529 5343 l 15537 5358 l 15545 5372 l 15553 5388 l 15559 5401 l 15565 5415 l 15572 5430 l 15579 5446 l 15585 5462 l 15592 5479 l 15599 5497 l 15606 5516 l 15613 5534 l 15619 5553 l 15626 5572 l 15632 5590 l 15637 5608 l 15643 5625 l 15648 5643 l 15653 5660 l 15657 5677 l 15662 5695 l 15666 5713 l 15671 5732 l 15675 5752 l 15679 5772 l 15684 5793 l 15688 5814 l 15691 5836 l 15695 5857 l 15698 5878 l 15701 5899 l 15704 5919 l 15706 5939 l 15708 5958 l 15710 5978 l 15711 5995 l 15713 6012 l 15714 6031 l 15715 6049 l 15716 6069 l 15717 6089 l 15717 6109 l 15718 6130 l 15719 6151 l 15719 6173 l 15719 6194 l 15720 6215 l 15720 6236 l 15720 6256 l 15720 6276 l 15720 6295 l 15720 6314 l 15720 6333 l 15720 6349 l 15720 6367 l 15720 6384 l 15720 6402 l 15720 6421 l 15720 6441 l 15720 6461 l 15720 6482 l 15720 6504 l 15720 6526 l 15720 6548 l 15721 6572 l 15721 6595 l 15721 6618 l 15721 6642 l 15721 6666 l 15722 6689 l 15722 6713 l 15722 6738 l 15723 6763 l 15723 6784 l 15723 6806 l 15723 6828 l 15724 6852 l 15724 6876 l 15725 6901 l 15725 6927 l 15726 6953 l 15726 6980 l 15727 7008 l 15727 7036 l 15728 7064 l 15728 7092 l 15728 7120 l 15729 7147 l 15729 7174 l 15730 7200 l 15730 7226 l 15731 7250 l 15731 7274 l 15732 7297 l 15732 7319 l 15732 7340 l 15733 7360 l 15733 7386 l 15733 7412 l 15733 7437 l 15734 7461 l 15734 7486 l 15734 7510 l 15734 7533 l 15735 7556 l 15735 7578 l 15735 7600 l 15735 7620 l 15735 7639 l 15735 7658 l 15735 7675 l 15735 7691 l 15735 7707 l 15735 7721 l 15735 7735 l 15735 7752 l 15735 7770 l 15735 7787 l 15735 7805 l 15735 7823 l 15735 7841 l 15734 7859 l 15734 7876 l 15734 7894 l 15733 7911 l 15732 7928 l 15732 7944 l 15731 7959 l 15730 7975 l 15729 7991 l 15728 8007 l 15726 8024 l 15725 8042 l 15723 8061 l 15722 8079 l 15720 8098 l 15718 8116 l 15717 8134 l 15715 8152 l 15714 8168 l 15712 8183 l 15711 8197 l 15710 8210 l 15709 8227 l 15708 8244 l 15707 8260 l 15706 8276 l 15706 8290 l 15705 8304 l 15705 8317 l 15705 8328 l 15705 8338 l 15705 8348 l 15705 8356 l 15705 8365 l 15705 8374 l 15705 8384 l 15706 8394 l 15706 8405 l 15707 8416 l 15708 8427 l 15709 8438 l 15710 8450 l 15711 8461 l 15713 8472 l 15714 8485 l 15716 8499 l 15718 8514 l 15720 8529 l 15721 8544 l 15723 8560 l 15725 8575 l 15726 8589 l 15727 8602 l 15728 8615 l 15728 8618 l 15728 8621 l 15727 8624 l 15727 8627 l 15725 8629 l 15724 8632 l 15721 8635 l 15718 8638 l 15713 8641 l 15707 8644 l 15700 8646 l 15692 8649 l 15682 8652 l 15670 8655 l 15656 8658 l 15640 8660 l 15622 8663 l 15602 8666 l 15579 8669 l 15554 8671 l 15526 8674 l 15495 8677 l 15462 8679 l 15425 8682 l 15385 8684 l 15342 8687 l 15296 8689 l 15247 8692 l 15194 8694 l 15137 8696 l 15078 8699 l 15014 8701 l 14947 8703 l 14877 8705 l 14803 8707 l 14725 8709 l 14644 8711 l 14558 8713 l 14470 8714 l 14377 8716 l 14281 8717 l 14180 8719 l 14076 8720 l 13968 8722 l 13856 8723 l 13740 8724 l 13619 8725 l 13494 8726 l 13365 8727 l 13231 8728 l 13092 8729 l 12948 8730 l 12873 8730 l 12798 8731 l 12721 8731 l 12643 8731 l 12563 8732 l 12482 8732 l 12399 8732 l 12315 8733 l 12230 8733 l 12143 8733 l 12054 8733 l 11965 8734 l 11873 8734 l 11781 8734 l 11686 8734 l 11591 8734 l 11494 8734 l 11395 8734 l 11295 8734 l 11194 8734 l 11091 8734 l 10987 8734 l 10882 8734 l 10775 8734 l 10667 8734 l 10558 8734 l 10448 8734 l 10336 8734 l 10223 8734 l 10109 8733 l 9994 8733 l 9878 8733 l 9760 8733 l 9642 8732 l 9523 8732 l 9403 8731 l 9282 8731 l 9160 8730 l 9037 8730 l 8914 8729 l 8790 8729 l 8665 8728 l 8540 8728 l 8414 8727 l 8287 8726 l 8161 8725 l 8034 8725 l 7906 8724 l 7779 8723 l 7651 8722 l 7523 8721 l 7395 8720 l 7267 8719 l 7140 8718 l 7012 8717 l 6884 8716 l 6757 8715 l 6630 8714 l 6503 8712 l 6377 8711 l 6251 8710 l 6126 8708 l 6001 8707 l 5877 8706 l 5754 8704 l 5631 8703 l 5509 8701 l 5388 8700 l 5268 8698 l 5149 8696 l 5031 8695 l 4913 8693 l 4797 8691 l 4682 8690 l 4568 8688 l 4455 8686 l 4343 8684 l 4233 8682 l 4124 8680 l 4016 8678 l 3909 8676 l 3804 8674 l 3700 8672 l 3597 8670 l 3496 8668 l 3396 8666 l 3298 8663 l 3201 8661 l 3105 8659 l 3011 8657 l 2918 8654 l 2827 8652 l 2737 8649 l 2649 8647 l 2562 8644 l 2477 8642 l 2393 8639 l 2310 8637 l 2229 8634 l 2150 8631 l 2071 8629 l 1995 8626 l 1919 8623 l 1845 8620 l 1701 8614 l 1562 8608 l 1428 8602 l 1299 8595 l 1174 8588 l 1054 8582 l 938 8574 l 826 8567 l 718 8560 l 614 8552 l 514 8544 l 417 8536 l 325 8528 l 236 8519 l 151 8511 l 70 8502 l -8 8493 l -81 8484 l -152 8475 l -218 8465 l -282 8456 l -341 8447 l -397 8437 l -450 8428 l -499 8418 l -545 8409 l -588 8399 l -628 8389 l -664 8380 l -698 8371 l -728 8361 l -756 8352 l -781 8343 l -804 8334 l -824 8325 l -842 8316 l -858 8307 l -872 8299 l -884 8291 l -894 8283 l -902 8275 l -909 8267 l -915 8260 l -919 8253 l -923 8246 l -926 8239 l -927 8232 l -929 8226 l -929 8220 l -930 8214 l -930 8208 l -930 8203 l -930 8177 l -930 8155 l -930 8138 l -930 8123 l -930 8111 l -929 8102 l -929 8096 l -929 8090 l -928 8085 l -928 8080 l -927 8075 l -926 8069 l -925 8062 l -924 8053 l -923 8042 l -922 8030 l -921 8016 l -920 8000 l -919 7983 l -917 7965 l -916 7946 l cp gs col7 0.75 shd ef gr gs col0 s gr [] 0 sd % Polyline 30.000 slw n 600 2715 m 600 6180 l gs col0 s gr % Polyline n 6300 2835 m 6285 6120 l gs col0 s gr % Polyline n 9045 2715 m 9045 2716 l 9044 2717 l 9042 2720 l 9040 2725 l 9037 2733 l 9033 2743 l 9029 2756 l 9024 2771 l 9020 2790 l 9015 2811 l 9011 2834 l 9007 2861 l 9004 2890 l 9000 2922 l 8998 2958 l 8995 2997 l 8993 3041 l 8991 3090 l 8990 3144 l 8989 3204 l 8988 3270 l 8987 3300 l 8987 3331 l 8986 3363 l 8986 3397 l 8986 3433 l 8986 3469 l 8986 3508 l 8986 3549 l 8985 3591 l 8985 3635 l 8985 3682 l 8985 3731 l 8986 3782 l 8986 3836 l 8986 3893 l 8986 3952 l 8986 4013 l 8986 4078 l 8987 4145 l 8987 4215 l 8988 4288 l 8988 4364 l 8988 4442 l 8989 4522 l 8989 4605 l 8990 4689 l 8991 4776 l 8991 4863 l 8992 4951 l 8992 5039 l 8993 5127 l 8994 5214 l 8994 5300 l 8995 5383 l 8995 5463 l 8996 5540 l 8997 5612 l 8997 5680 l 8998 5742 l 8998 5799 l 8998 5849 l 8999 5893 l 8999 5931 l 8999 5963 l 9000 5988 l 9000 6009 l 9000 6023 l 9000 6034 l 9000 6040 l 9000 6044 l 9000 6045 l gs col0 s gr % Polyline n 14385 2910 m 14415 6015 l gs col0 s gr % Polyline 15.000 slw n 600 2400 m 6300 2400 l 6300 6600 l 600 6600 l cp gs col0 s gr % Polyline 7.500 slw [60 30 15 30] 0 sd n 9000 5400 m 14400 5400 l 14400 6600 l 9000 6600 l cp gs col0 s gr [] 0 sd % Polyline [60 30 15 30] 0 sd n 9000 2400 m 14400 2400 l 14400 3600 l 9000 3600 l cp gs col0 s gr [] 0 sd % Polyline [60 30 15 30] 0 sd n 600 5400 m 6300 5400 l 6300 6600 l 600 6600 l cp gs col0 s gr [] 0 sd % Polyline [60 30 15 30] 0 sd n 600 2400 m 6300 2400 l 6300 3600 l 600 3600 l cp gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd n 600 4500 m 6300 4500 l gs col0 s gr [] 0 sd % Polyline [15 45] 45 sd n 9000 4500 m 14400 4500 l gs col0 s gr [] 0 sd % Polyline 1 slj 30.000 slw n 9000 2400 m 14400 2400 l 14400 6600 l 9000 6600 l cp gs col0 s gr % Polyline 0 slj n 9000 6045 m 9004 6047 l 9011 6051 l 9025 6057 l 9044 6067 l 9068 6079 l 9096 6092 l 9125 6107 l 9155 6121 l 9183 6135 l 9210 6147 l 9234 6159 l 9257 6170 l 9277 6179 l 9296 6188 l 9314 6196 l 9331 6203 l 9348 6210 l 9364 6217 l 9380 6223 l 9397 6230 l 9414 6236 l 9431 6242 l 9449 6248 l 9468 6254 l 9487 6259 l 9506 6264 l 9525 6268 l 9544 6272 l 9564 6276 l 9583 6279 l 9603 6281 l 9622 6283 l 9641 6284 l 9660 6285 l 9680 6285 l 9698 6285 l 9717 6284 l 9736 6283 l 9757 6282 l 9778 6280 l 9800 6277 l 9823 6274 l 9847 6271 l 9871 6267 l 9895 6263 l 9920 6258 l 9944 6253 l 9969 6248 l 9993 6243 l 10016 6237 l 10039 6231 l 10061 6225 l 10083 6218 l 10104 6212 l 10125 6205 l 10146 6198 l 10166 6191 l 10187 6183 l 10208 6175 l 10230 6166 l 10252 6157 l 10274 6148 l 10297 6138 l 10320 6128 l 10344 6118 l 10367 6108 l 10390 6098 l 10413 6088 l 10436 6078 l 10459 6068 l 10481 6058 l 10503 6049 l 10524 6040 l 10546 6031 l 10568 6023 l 10587 6015 l 10608 6007 l 10628 5999 l 10650 5991 l 10672 5984 l 10694 5976 l 10717 5968 l 10741 5960 l 10764 5952 l 10788 5945 l 10813 5937 l 10837 5930 l 10860 5923 l 10884 5916 l 10906 5910 l 10928 5903 l 10950 5898 l 10970 5893 l 10990 5888 l 11009 5883 l 11027 5879 l 11045 5875 l 11069 5870 l 11092 5866 l 11115 5862 l 11138 5858 l 11160 5855 l 11183 5853 l 11205 5851 l 11226 5850 l 11247 5850 l 11267 5851 l 11285 5852 l 11303 5854 l 11319 5856 l 11335 5859 l 11349 5863 l 11363 5868 l 11377 5873 l 11392 5880 l 11407 5888 l 11421 5897 l 11435 5907 l 11448 5918 l 11462 5930 l 11474 5942 l 11486 5954 l 11496 5967 l 11506 5979 l 11515 5991 l 11523 6003 l 11530 6015 l 11538 6029 l 11545 6043 l 11552 6057 l 11558 6072 l 11564 6088 l 11569 6103 l 11574 6117 l 11579 6131 l 11583 6144 l 11586 6156 l 11590 6167 l 11593 6178 l 11596 6189 l 11599 6200 l 11603 6210 l 11607 6220 l 11611 6230 l 11615 6239 l 11619 6248 l 11623 6256 l 11628 6263 l 11633 6270 l 11638 6277 l 11643 6284 l 11650 6292 l 11657 6299 l 11664 6307 l 11672 6315 l 11680 6322 l 11689 6330 l 11697 6336 l 11705 6343 l 11713 6349 l 11723 6355 l 11732 6361 l 11743 6367 l 11754 6373 l 11766 6379 l 11778 6384 l 11789 6388 l 11801 6392 l 11813 6395 l 11824 6397 l 11837 6399 l 11851 6401 l 11865 6401 l 11879 6400 l 11893 6398 l 11906 6395 l 11919 6391 l 11930 6386 l 11940 6380 l 11949 6372 l 11958 6363 l 11966 6353 l 11974 6341 l 11982 6328 l 11988 6315 l 11994 6301 l 11998 6288 l 12002 6276 l 12005 6265 l 12007 6254 l 12009 6243 l 12011 6232 l 12012 6221 l 12012 6210 l 12012 6199 l 12011 6188 l 12009 6177 l 12007 6166 l 12005 6155 l 12003 6146 l 12000 6136 l 11996 6125 l 11993 6113 l 11989 6101 l 11985 6088 l 11980 6074 l 11976 6061 l 11972 6047 l 11969 6034 l 11966 6021 l 11963 6008 l 11960 5994 l 11957 5980 l 11955 5965 l 11953 5950 l 11952 5934 l 11951 5917 l 11950 5901 l 11950 5885 l 11950 5870 l 11951 5855 l 11953 5841 l 11955 5828 l 11958 5814 l 11961 5801 l 11965 5788 l 11969 5775 l 11975 5761 l 11981 5748 l 11987 5735 l 11994 5724 l 12001 5713 l 12008 5702 l 12015 5693 l 12023 5685 l 12030 5677 l 12038 5670 l 12047 5663 l 12057 5656 l 12067 5650 l 12078 5644 l 12090 5639 l 12102 5634 l 12115 5630 l 12127 5627 l 12140 5624 l 12153 5623 l 12164 5621 l 12176 5620 l 12190 5619 l 12204 5619 l 12219 5619 l 12235 5619 l 12251 5619 l 12268 5619 l 12286 5620 l 12303 5620 l 12320 5621 l 12337 5621 l 12353 5622 l 12370 5623 l 12385 5623 l 12400 5623 l 12416 5624 l 12432 5624 l 12449 5625 l 12466 5626 l 12484 5627 l 12502 5628 l 12520 5630 l 12537 5632 l 12554 5634 l 12571 5636 l 12586 5639 l 12602 5642 l 12616 5646 l 12630 5650 l 12646 5655 l 12661 5661 l 12676 5668 l 12692 5676 l 12707 5685 l 12722 5694 l 12737 5704 l 12750 5714 l 12763 5725 l 12775 5736 l 12786 5746 l 12796 5757 l 12805 5767 l 12813 5778 l 12821 5790 l 12828 5802 l 12834 5815 l 12840 5829 l 12845 5843 l 12849 5858 l 12852 5872 l 12854 5886 l 12855 5900 l 12855 5913 l 12854 5925 l 12853 5938 l 12850 5950 l 12848 5962 l 12845 5974 l 12841 5987 l 12838 6001 l 12835 6014 l 12832 6028 l 12829 6041 l 12827 6053 l 12826 6065 l 12826 6077 l 12828 6088 l 12830 6101 l 12835 6114 l 12842 6127 l 12850 6141 l 12860 6154 l 12871 6166 l 12882 6177 l 12894 6186 l 12906 6194 l 12918 6200 l 12925 6203 l 12933 6206 l 12941 6208 l 12949 6209 l 12959 6210 l 12969 6210 l 12980 6209 l 12992 6207 l 13005 6204 l 13018 6200 l 13032 6195 l 13047 6189 l 13063 6183 l 13079 6175 l 13097 6167 l 13115 6158 l 13131 6149 l 13147 6140 l 13165 6130 l 13184 6120 l 13203 6109 l 13224 6096 l 13246 6084 l 13269 6071 l 13292 6057 l 13316 6043 l 13339 6029 l 13363 6015 l 13387 6001 l 13410 5988 l 13432 5974 l 13454 5962 l 13475 5950 l 13495 5939 l 13514 5928 l 13533 5918 l 13555 5905 l 13577 5894 l 13598 5883 l 13620 5873 l 13641 5863 l 13661 5853 l 13682 5845 l 13701 5837 l 13720 5830 l 13738 5824 l 13755 5819 l 13771 5815 l 13786 5812 l 13800 5810 l 13813 5808 l 13825 5808 l 13836 5807 l 13846 5808 l 13856 5809 l 13866 5811 l 13875 5813 l 13885 5816 l 13894 5820 l 13902 5824 l 13910 5830 l 13917 5836 l 13923 5842 l 13929 5849 l 13933 5857 l 13937 5865 l 13940 5874 l 13942 5883 l 13942 5892 l 13943 5903 l 13941 5916 l 13939 5931 l 13935 5948 l 13930 5965 l 13925 5984 l 13919 6003 l 13912 6023 l 13906 6043 l 13900 6062 l 13895 6081 l 13890 6099 l 13886 6115 l 13884 6131 l 13883 6145 l 13883 6158 l 13884 6171 l 13887 6183 l 13892 6195 l 13897 6206 l 13904 6216 l 13912 6226 l 13921 6234 l 13930 6242 l 13939 6249 l 13949 6256 l 13959 6261 l 13968 6266 l 13978 6270 l 13988 6274 l 13999 6278 l 14011 6281 l 14023 6284 l 14035 6285 l 14047 6286 l 14059 6286 l 14071 6284 l 14083 6281 l 14094 6278 l 14105 6273 l 14115 6268 l 14124 6262 l 14133 6255 l 14142 6247 l 14152 6238 l 14162 6228 l 14173 6218 l 14183 6207 l 14194 6195 l 14205 6183 l 14215 6171 l 14225 6160 l 14235 6149 l 14245 6138 l 14255 6128 l 14267 6116 l 14279 6104 l 14291 6092 l 14304 6080 l 14316 6068 l 14329 6057 l 14341 6047 l 14351 6038 l 14361 6030 l 14370 6023 l 14377 6017 l 14383 6013 l 14384 6011 l 14386 6010 l 14387 6009 l 14388 6008 l 14389 6007 l 14390 6007 l 14391 6006 l 14392 6006 l 14392 6005 l 14393 6005 l 14394 6005 l 14393 6005 l 14393 6006 l 14392 6007 l 14392 6008 l 14391 6008 l 14390 6009 l 14390 6010 l 14389 6011 l 14388 6011 l 14388 6012 l 14387 6013 l 14386 6014 l 14385 6015 l gs col0 s gr % Polyline n 9015 2715 m 9017 2717 l 9021 2722 l 9029 2730 l 9040 2743 l 9056 2760 l 9074 2780 l 9095 2803 l 9118 2828 l 9141 2853 l 9164 2878 l 9187 2902 l 9209 2924 l 9229 2945 l 9248 2965 l 9266 2982 l 9282 2998 l 9298 3013 l 9313 3027 l 9327 3039 l 9341 3051 l 9355 3063 l 9372 3076 l 9389 3088 l 9406 3100 l 9423 3112 l 9441 3123 l 9459 3134 l 9477 3144 l 9496 3154 l 9514 3164 l 9532 3173 l 9550 3181 l 9567 3188 l 9583 3195 l 9599 3201 l 9614 3207 l 9628 3212 l 9642 3216 l 9655 3220 l 9671 3225 l 9688 3229 l 9704 3233 l 9721 3236 l 9737 3239 l 9754 3241 l 9771 3243 l 9788 3244 l 9804 3245 l 9820 3245 l 9836 3245 l 9851 3245 l 9865 3244 l 9880 3243 l 9895 3241 l 9910 3239 l 9927 3236 l 9944 3233 l 9961 3230 l 9979 3226 l 9998 3222 l 10016 3217 l 10035 3212 l 10053 3206 l 10070 3201 l 10086 3195 l 10102 3189 l 10118 3183 l 10133 3176 l 10148 3169 l 10164 3161 l 10179 3153 l 10196 3144 l 10212 3134 l 10228 3124 l 10244 3114 l 10260 3103 l 10275 3093 l 10290 3082 l 10304 3071 l 10317 3061 l 10330 3050 l 10341 3040 l 10352 3030 l 10364 3020 l 10376 3009 l 10388 2998 l 10400 2987 l 10413 2975 l 10426 2963 l 10440 2951 l 10453 2939 l 10466 2928 l 10479 2917 l 10492 2906 l 10505 2896 l 10517 2887 l 10530 2878 l 10543 2869 l 10557 2860 l 10571 2851 l 10586 2843 l 10602 2834 l 10618 2826 l 10636 2818 l 10653 2810 l 10671 2803 l 10689 2796 l 10707 2790 l 10725 2785 l 10742 2780 l 10759 2776 l 10776 2773 l 10793 2770 l 10809 2768 l 10827 2766 l 10845 2764 l 10863 2763 l 10882 2763 l 10902 2763 l 10921 2763 l 10941 2764 l 10961 2765 l 10981 2766 l 11000 2768 l 11019 2769 l 11036 2771 l 11053 2773 l 11069 2775 l 11085 2778 l 11103 2780 l 11120 2783 l 11138 2786 l 11156 2789 l 11174 2793 l 11192 2797 l 11211 2802 l 11229 2807 l 11247 2812 l 11264 2819 l 11281 2825 l 11297 2832 l 11312 2839 l 11328 2848 l 11341 2855 l 11355 2863 l 11369 2872 l 11383 2882 l 11399 2893 l 11415 2904 l 11431 2915 l 11448 2927 l 11465 2939 l 11482 2951 l 11499 2963 l 11516 2975 l 11533 2986 l 11549 2997 l 11566 3007 l 11583 3018 l 11598 3026 l 11613 3035 l 11629 3043 l 11646 3052 l 11664 3061 l 11683 3069 l 11702 3078 l 11722 3087 l 11742 3095 l 11763 3103 l 11783 3111 l 11804 3119 l 11825 3127 l 11845 3134 l 11866 3141 l 11885 3147 l 11905 3154 l 11925 3160 l 11941 3165 l 11958 3170 l 11975 3175 l 11993 3180 l 12012 3185 l 12031 3190 l 12051 3195 l 12072 3201 l 12093 3206 l 12115 3211 l 12138 3216 l 12162 3222 l 12185 3227 l 12209 3232 l 12234 3237 l 12258 3242 l 12282 3246 l 12307 3251 l 12332 3255 l 12357 3259 l 12382 3263 l 12408 3268 l 12430 3271 l 12453 3274 l 12476 3278 l 12500 3281 l 12526 3285 l 12551 3288 l 12578 3291 l 12606 3294 l 12634 3298 l 12663 3301 l 12692 3303 l 12721 3306 l 12751 3309 l 12781 3311 l 12810 3313 l 12840 3315 l 12869 3317 l 12897 3318 l 12925 3319 l 12952 3320 l 12979 3320 l 13004 3320 l 13029 3320 l 13053 3319 l 13077 3319 l 13100 3318 l 13127 3316 l 13153 3313 l 13179 3311 l 13205 3307 l 13231 3304 l 13256 3299 l 13282 3295 l 13307 3290 l 13333 3284 l 13357 3278 l 13382 3272 l 13406 3265 l 13429 3259 l 13451 3252 l 13472 3245 l 13492 3238 l 13512 3231 l 13530 3224 l 13547 3217 l 13564 3211 l 13580 3204 l 13595 3198 l 13615 3188 l 13635 3179 l 13655 3170 l 13674 3161 l 13693 3151 l 13712 3141 l 13731 3131 l 13750 3120 l 13768 3110 l 13785 3100 l 13802 3090 l 13818 3081 l 13834 3071 l 13849 3062 l 13863 3054 l 13878 3045 l 13892 3036 l 13906 3028 l 13921 3019 l 13936 3010 l 13952 3000 l 13968 2991 l 13984 2982 l 14001 2973 l 14017 2964 l 14033 2955 l 14048 2947 l 14063 2940 l 14077 2933 l 14090 2926 l 14103 2920 l 14115 2915 l 14131 2908 l 14147 2903 l 14162 2897 l 14178 2892 l 14193 2888 l 14208 2885 l 14223 2882 l 14236 2880 l 14249 2878 l 14260 2877 l 14271 2877 l 14280 2878 l 14293 2879 l 14306 2882 l 14320 2886 l 14335 2893 l 14350 2900 l 14363 2906 l 14369 2909 l 14370 2910 l gs col0 s gr % Polyline n 8970 4335 m 8969 4335 l 8965 4332 l 8957 4326 l 8945 4317 l 8932 4308 l 8919 4298 l 8909 4290 l 8900 4282 l 8892 4275 l 8885 4268 l 8878 4260 l 8871 4251 l 8864 4242 l 8856 4232 l 8847 4222 l 8838 4213 l 8828 4203 l 8818 4194 l 8807 4185 l 8795 4178 l 8784 4171 l 8772 4165 l 8759 4160 l 8744 4154 l 8729 4149 l 8712 4145 l 8695 4142 l 8678 4139 l 8662 4138 l 8646 4138 l 8630 4138 l 8615 4140 l 8604 4142 l 8593 4145 l 8581 4148 l 8570 4153 l 8558 4158 l 8547 4164 l 8535 4171 l 8523 4178 l 8512 4187 l 8502 4196 l 8491 4205 l 8482 4216 l 8473 4226 l 8465 4237 l 8457 4248 l 8450 4260 l 8443 4272 l 8437 4286 l 8431 4300 l 8425 4316 l 8420 4332 l 8415 4351 l 8411 4370 l 8407 4390 l 8404 4412 l 8402 4434 l 8400 4457 l 8399 4480 l 8399 4503 l 8400 4527 l 8401 4550 l 8403 4575 l 8404 4593 l 8406 4612 l 8409 4632 l 8412 4653 l 8415 4674 l 8418 4696 l 8422 4719 l 8426 4742 l 8431 4766 l 8435 4790 l 8440 4815 l 8445 4839 l 8450 4863 l 8455 4887 l 8460 4910 l 8465 4933 l 8470 4955 l 8475 4976 l 8480 4996 l 8484 5016 l 8488 5034 l 8493 5053 l 8497 5074 l 8502 5095 l 8507 5116 l 8511 5137 l 8516 5157 l 8520 5178 l 8524 5200 l 8528 5221 l 8532 5242 l 8536 5263 l 8539 5285 l 8543 5306 l 8546 5327 l 8549 5347 l 8551 5368 l 8553 5388 l 8556 5409 l 8558 5430 l 8559 5450 l 8561 5470 l 8562 5491 l 8564 5513 l 8565 5537 l 8566 5561 l 8567 5586 l 8568 5611 l 8568 5638 l 8569 5664 l 8569 5691 l 8569 5717 l 8569 5744 l 8568 5769 l 8567 5794 l 8566 5818 l 8565 5842 l 8564 5864 l 8562 5886 l 8560 5908 l 8558 5926 l 8556 5945 l 8553 5964 l 8550 5983 l 8547 6003 l 8544 6023 l 8540 6043 l 8536 6064 l 8531 6085 l 8526 6107 l 8521 6130 l 8516 6153 l 8510 6176 l 8504 6200 l 8498 6224 l 8492 6248 l 8485 6273 l 8478 6298 l 8472 6323 l 8465 6349 l 8457 6375 l 8450 6403 l 8444 6425 l 8438 6448 l 8431 6472 l 8425 6496 l 8418 6522 l 8411 6549 l 8404 6576 l 8397 6605 l 8389 6634 l 8382 6664 l 8374 6695 l 8367 6726 l 8359 6758 l 8352 6790 l 8344 6821 l 8337 6853 l 8330 6885 l 8323 6916 l 8317 6946 l 8311 6976 l 8305 7006 l 8300 7034 l 8295 7062 l 8290 7088 l 8286 7114 l 8282 7140 l 8278 7164 l 8275 7188 l 8272 7217 l 8269 7245 l 8266 7273 l 8265 7301 l 8264 7329 l 8264 7356 l 8264 7383 l 8265 7409 l 8267 7436 l 8269 7462 l 8273 7487 l 8277 7512 l 8281 7536 l 8287 7559 l 8293 7582 l 8299 7604 l 8307 7625 l 8314 7645 l 8322 7664 l 8331 7683 l 8340 7702 l 8350 7720 l 8359 7737 l 8370 7753 l 8380 7770 l 8392 7787 l 8405 7804 l 8418 7822 l 8433 7840 l 8448 7857 l 8465 7875 l 8483 7893 l 8502 7911 l 8522 7929 l 8543 7947 l 8564 7964 l 8587 7981 l 8610 7997 l 8634 8013 l 8659 8028 l 8684 8043 l 8710 8057 l 8736 8070 l 8763 8083 l 8791 8096 l 8820 8108 l 8844 8117 l 8868 8126 l 8894 8135 l 8920 8144 l 8948 8152 l 8976 8161 l 9006 8169 l 9037 8178 l 9068 8186 l 9101 8194 l 9135 8202 l 9169 8209 l 9205 8217 l 9240 8224 l 9277 8231 l 9313 8237 l 9350 8244 l 9387 8249 l 9424 8255 l 9461 8260 l 9498 8265 l 9534 8269 l 9570 8274 l 9605 8277 l 9640 8281 l 9674 8284 l 9708 8286 l 9742 8289 l 9775 8291 l 9808 8293 l 9838 8294 l 9869 8295 l 9900 8296 l 9931 8297 l 9963 8297 l 9994 8297 l 10027 8297 l 10060 8296 l 10093 8296 l 10126 8294 l 10160 8293 l 10195 8291 l 10230 8289 l 10264 8287 l 10300 8284 l 10335 8281 l 10370 8278 l 10405 8275 l 10440 8271 l 10474 8267 l 10509 8262 l 10543 8258 l 10576 8253 l 10609 8248 l 10642 8243 l 10674 8237 l 10706 8232 l 10737 8226 l 10768 8220 l 10799 8213 l 10830 8207 l 10860 8200 l 10889 8193 l 10918 8187 l 10947 8179 l 10977 8172 l 11007 8164 l 11037 8157 l 11069 8148 l 11101 8140 l 11133 8131 l 11166 8122 l 11200 8113 l 11234 8104 l 11269 8095 l 11304 8085 l 11340 8075 l 11376 8065 l 11412 8056 l 11449 8046 l 11486 8036 l 11523 8027 l 11560 8017 l 11597 8008 l 11634 7999 l 11671 7990 l 11707 7981 l 11744 7972 l 11780 7964 l 11816 7956 l 11852 7949 l 11887 7941 l 11923 7934 l 11959 7928 l 11994 7921 l 12030 7915 l 12064 7909 l 12099 7904 l 12134 7899 l 12169 7894 l 12206 7889 l 12243 7884 l 12280 7880 l 12319 7876 l 12358 7872 l 12397 7868 l 12437 7865 l 12478 7862 l 12519 7859 l 12561 7857 l 12603 7854 l 12645 7853 l 12688 7851 l 12730 7850 l 12772 7849 l 12815 7848 l 12856 7848 l 12898 7848 l 12939 7849 l 12979 7850 l 13019 7851 l 13058 7853 l 13096 7855 l 13133 7857 l 13170 7860 l 13206 7863 l 13241 7866 l 13275 7870 l 13309 7874 l 13341 7878 l 13373 7883 l 13405 7888 l 13440 7894 l 13475 7900 l 13509 7907 l 13543 7914 l 13577 7922 l 13611 7931 l 13645 7940 l 13679 7949 l 13713 7958 l 13748 7968 l 13782 7979 l 13816 7989 l 13850 8000 l 13884 8012 l 13918 8023 l 13952 8034 l 13985 8046 l 14018 8057 l 14051 8068 l 14083 8080 l 14115 8091 l 14146 8101 l 14176 8112 l 14206 8122 l 14236 8132 l 14265 8141 l 14293 8151 l 14321 8159 l 14349 8168 l 14376 8175 l 14403 8183 l 14430 8190 l 14461 8198 l 14492 8205 l 14524 8211 l 14556 8217 l 14588 8223 l 14621 8228 l 14655 8232 l 14688 8236 l 14722 8239 l 14756 8241 l 14791 8242 l 14825 8243 l 14859 8243 l 14892 8241 l 14925 8239 l 14958 8236 l 14989 8232 l 15020 8227 l 15050 8222 l 15078 8215 l 15106 8207 l 15132 8199 l 15157 8190 l 15180 8179 l 15202 8168 l 15224 8157 l 15244 8144 l 15263 8130 l 15279 8116 l 15295 8102 l 15311 8086 l 15325 8069 l 15339 8051 l 15353 8031 l 15366 8011 l 15378 7988 l 15390 7965 l 15401 7940 l 15412 7914 l 15422 7887 l 15431 7858 l 15440 7829 l 15448 7798 l 15455 7766 l 15462 7733 l 15469 7699 l 15474 7665 l 15479 7630 l 15484 7595 l 15488 7559 l 15491 7522 l 15494 7486 l 15497 7449 l 15499 7411 l 15501 7374 l 15503 7335 l 15504 7297 l 15505 7258 l 15506 7226 l 15506 7194 l 15507 7161 l 15507 7127 l 15507 7093 l 15507 7058 l 15506 7022 l 15505 6985 l 15505 6947 l 15503 6908 l 15502 6868 l 15500 6828 l 15498 6787 l 15496 6745 l 15493 6702 l 15490 6659 l 15486 6616 l 15482 6572 l 15478 6528 l 15473 6483 l 15468 6439 l 15463 6394 l 15457 6349 l 15451 6305 l 15444 6261 l 15437 6218 l 15430 6174 l 15422 6132 l 15414 6089 l 15405 6048 l 15396 6006 l 15387 5966 l 15377 5926 l 15367 5886 l 15357 5847 l 15346 5809 l 15334 5770 l 15323 5733 l 15309 5693 l 15296 5653 l 15281 5613 l 15266 5573 l 15251 5533 l 15235 5493 l 15218 5453 l 15200 5413 l 15182 5372 l 15163 5332 l 15144 5292 l 15124 5251 l 15104 5211 l 15084 5171 l 15063 5131 l 15042 5092 l 15020 5054 l 14999 5016 l 14978 4979 l 14956 4942 l 14935 4907 l 14914 4873 l 14893 4839 l 14873 4807 l 14853 4777 l 14834 4747 l 14815 4719 l 14796 4692 l 14778 4667 l 14761 4643 l 14744 4620 l 14728 4598 l 14713 4578 l 14698 4559 l 14684 4542 l 14670 4525 l 14651 4502 l 14632 4482 l 14615 4464 l 14599 4449 l 14584 4436 l 14570 4425 l 14556 4416 l 14542 4409 l 14529 4404 l 14516 4401 l 14503 4399 l 14491 4399 l 14478 4400 l 14467 4402 l 14456 4405 l 14446 4408 l 14437 4412 l 14430 4416 l 14424 4419 l 14420 4422 l 14417 4423 l 14416 4425 l 14415 4425 l gs col0 s gr % Polyline n 585 4440 m 584 4440 l 576 4440 l 565 4440 l 554 4440 l 545 4440 l 538 4440 l 531 4440 l 524 4439 l 515 4438 l 505 4435 l 493 4430 l 480 4423 l 464 4414 l 448 4403 l 438 4396 l 428 4388 l 417 4380 l 405 4370 l 392 4360 l 378 4350 l 363 4339 l 348 4329 l 332 4318 l 317 4307 l 301 4297 l 285 4288 l 270 4280 l 254 4272 l 240 4266 l 225 4260 l 210 4255 l 195 4251 l 180 4248 l 164 4246 l 148 4245 l 131 4244 l 114 4245 l 97 4246 l 80 4248 l 63 4250 l 46 4253 l 29 4257 l 13 4261 l -2 4265 l -17 4270 l -33 4275 l -48 4280 l -63 4286 l -79 4293 l -95 4300 l -112 4308 l -129 4317 l -147 4326 l -165 4337 l -182 4348 l -200 4360 l -217 4373 l -234 4387 l -250 4401 l -265 4416 l -280 4431 l -295 4448 l -307 4461 l -318 4476 l -330 4491 l -342 4508 l -354 4525 l -366 4544 l -378 4563 l -389 4584 l -401 4605 l -412 4626 l -423 4648 l -433 4670 l -442 4692 l -451 4714 l -459 4736 l -466 4757 l -473 4778 l -478 4798 l -483 4818 l -488 4838 l -491 4857 l -494 4877 l -496 4897 l -497 4917 l -498 4938 l -498 4960 l -498 4981 l -497 5004 l -495 5026 l -492 5049 l -489 5072 l -486 5095 l -482 5118 l -478 5140 l -473 5163 l -468 5185 l -462 5206 l -457 5228 l -451 5249 l -445 5270 l -439 5290 l -433 5309 l -427 5330 l -420 5351 l -414 5373 l -407 5396 l -399 5419 l -392 5443 l -385 5468 l -377 5493 l -370 5519 l -362 5545 l -355 5571 l -348 5598 l -341 5624 l -335 5650 l -329 5676 l -323 5702 l -318 5727 l -313 5752 l -309 5777 l -305 5803 l -302 5826 l -299 5850 l -296 5874 l -294 5899 l -292 5925 l -290 5951 l -289 5978 l -288 6006 l -288 6034 l -288 6062 l -288 6091 l -289 6120 l -290 6149 l -292 6178 l -294 6207 l -297 6235 l -300 6263 l -304 6290 l -307 6317 l -312 6343 l -316 6368 l -321 6392 l -327 6416 l -333 6440 l -339 6463 l -345 6487 l -353 6510 l -360 6534 l -368 6558 l -376 6583 l -385 6609 l -394 6634 l -403 6661 l -412 6687 l -421 6715 l -430 6742 l -439 6770 l -447 6798 l -455 6827 l -463 6855 l -470 6883 l -476 6911 l -482 6940 l -487 6968 l -491 6996 l -495 7025 l -498 7053 l -500 7083 l -501 7108 l -502 7134 l -502 7161 l -501 7189 l -500 7217 l -498 7247 l -495 7277 l -491 7308 l -487 7339 l -482 7371 l -475 7403 l -469 7436 l -461 7469 l -452 7502 l -443 7534 l -433 7567 l -422 7598 l -410 7630 l -398 7660 l -385 7690 l -371 7718 l -357 7746 l -343 7773 l -327 7798 l -311 7823 l -295 7846 l -278 7868 l -260 7890 l -241 7911 l -222 7931 l -202 7950 l -180 7969 l -158 7987 l -135 8005 l -110 8023 l -85 8040 l -59 8056 l -32 8072 l -4 8088 l 24 8103 l 53 8118 l 82 8131 l 112 8145 l 141 8157 l 171 8169 l 200 8180 l 229 8191 l 257 8201 l 285 8211 l 312 8219 l 339 8228 l 365 8235 l 390 8243 l 415 8250 l 439 8256 l 463 8263 l 489 8270 l 516 8276 l 542 8283 l 569 8289 l 595 8295 l 622 8301 l 648 8307 l 675 8312 l 702 8317 l 728 8322 l 755 8326 l 782 8330 l 808 8334 l 834 8337 l 859 8340 l 885 8343 l 909 8345 l 933 8346 l 957 8347 l 980 8348 l 1003 8348 l 1025 8349 l 1048 8348 l 1070 8348 l 1092 8346 l 1115 8345 l 1138 8343 l 1162 8341 l 1187 8339 l 1211 8336 l 1237 8332 l 1263 8328 l 1289 8324 l 1315 8320 l 1342 8315 l 1368 8310 l 1395 8304 l 1421 8298 l 1446 8292 l 1472 8286 l 1496 8279 l 1520 8272 l 1542 8266 l 1564 8259 l 1586 8252 l 1606 8245 l 1626 8237 l 1645 8230 l 1665 8222 l 1685 8213 l 1705 8204 l 1726 8195 l 1746 8185 l 1766 8175 l 1787 8165 l 1809 8154 l 1831 8143 l 1853 8132 l 1875 8120 l 1898 8108 l 1922 8097 l 1945 8085 l 1969 8073 l 1994 8062 l 2018 8051 l 2043 8040 l 2068 8029 l 2094 8018 l 2120 8008 l 2148 7998 l 2170 7989 l 2193 7981 l 2217 7973 l 2242 7965 l 2268 7957 l 2295 7948 l 2323 7940 l 2352 7932 l 2383 7924 l 2414 7915 l 2446 7907 l 2478 7899 l 2511 7891 l 2545 7884 l 2579 7876 l 2613 7869 l 2647 7862 l 2681 7856 l 2715 7850 l 2748 7844 l 2781 7839 l 2813 7834 l 2845 7830 l 2876 7826 l 2906 7823 l 2936 7820 l 2966 7817 l 2995 7815 l 3024 7813 l 3053 7812 l 3082 7811 l 3111 7810 l 3140 7810 l 3170 7811 l 3200 7811 l 3230 7812 l 3261 7814 l 3291 7816 l 3323 7818 l 3354 7821 l 3385 7824 l 3417 7828 l 3448 7832 l 3479 7837 l 3510 7841 l 3540 7846 l 3570 7852 l 3600 7857 l 3629 7863 l 3657 7869 l 3685 7876 l 3713 7882 l 3740 7889 l 3767 7896 l 3793 7903 l 3820 7910 l 3845 7917 l 3870 7924 l 3895 7932 l 3921 7939 l 3947 7947 l 3974 7956 l 4002 7964 l 4030 7973 l 4059 7982 l 4088 7991 l 4118 8000 l 4149 8009 l 4181 8019 l 4213 8028 l 4245 8038 l 4278 8047 l 4311 8056 l 4344 8065 l 4377 8074 l 4411 8083 l 4444 8091 l 4478 8100 l 4512 8107 l 4545 8115 l 4578 8122 l 4612 8129 l 4646 8135 l 4679 8141 l 4713 8147 l 4748 8153 l 4780 8157 l 4814 8162 l 4848 8166 l 4882 8170 l 4918 8174 l 4954 8178 l 4991 8181 l 5029 8184 l 5068 8186 l 5107 8189 l 5146 8191 l 5186 8193 l 5226 8194 l 5267 8195 l 5307 8196 l 5347 8197 l 5387 8197 l 5426 8196 l 5465 8196 l 5503 8195 l 5540 8193 l 5576 8192 l 5611 8190 l 5644 8187 l 5677 8185 l 5708 8182 l 5738 8178 l 5766 8175 l 5793 8171 l 5819 8167 l 5844 8162 l 5868 8158 l 5900 8150 l 5930 8142 l 5959 8133 l 5986 8123 l 6011 8112 l 6035 8101 l 6058 8089 l 6079 8076 l 6098 8063 l 6116 8049 l 6133 8035 l 6148 8020 l 6161 8006 l 6173 7991 l 6184 7977 l 6193 7963 l 6201 7949 l 6209 7935 l 6215 7922 l 6220 7909 l 6225 7897 l 6230 7885 l 6236 7869 l 6241 7853 l 6247 7837 l 6252 7822 l 6258 7806 l 6263 7790 l 6270 7775 l 6277 7760 l 6284 7745 l 6292 7731 l 6301 7718 l 6310 7705 l 6321 7693 l 6332 7681 l 6344 7670 l 6358 7660 l 6371 7651 l 6385 7642 l 6401 7633 l 6419 7624 l 6438 7616 l 6458 7607 l 6480 7599 l 6502 7592 l 6526 7585 l 6550 7578 l 6574 7573 l 6599 7568 l 6623 7564 l 6647 7562 l 6670 7560 l 6693 7559 l 6716 7559 l 6738 7560 l 6759 7562 l 6781 7565 l 6803 7569 l 6825 7573 l 6848 7579 l 6870 7585 l 6893 7591 l 6916 7598 l 6938 7605 l 6960 7612 l 6982 7619 l 7002 7626 l 7022 7632 l 7040 7638 l 7058 7643 l 7075 7647 l 7090 7650 l 7105 7653 l 7121 7654 l 7137 7654 l 7152 7654 l 7167 7651 l 7182 7648 l 7196 7643 l 7210 7637 l 7224 7630 l 7237 7621 l 7249 7612 l 7261 7601 l 7272 7590 l 7282 7579 l 7292 7566 l 7301 7553 l 7310 7540 l 7316 7530 l 7322 7519 l 7328 7507 l 7335 7495 l 7341 7481 l 7347 7466 l 7353 7450 l 7359 7432 l 7364 7412 l 7370 7391 l 7375 7369 l 7381 7344 l 7386 7318 l 7391 7291 l 7395 7262 l 7399 7232 l 7403 7200 l 7407 7167 l 7410 7133 l 7413 7097 l 7415 7060 l 7418 7020 l 7419 6995 l 7420 6969 l 7421 6941 l 7422 6913 l 7423 6884 l 7424 6853 l 7424 6822 l 7425 6789 l 7425 6755 l 7425 6721 l 7425 6685 l 7425 6648 l 7425 6610 l 7425 6571 l 7424 6532 l 7423 6492 l 7422 6452 l 7421 6411 l 7419 6370 l 7418 6328 l 7416 6287 l 7414 6246 l 7411 6204 l 7409 6164 l 7406 6123 l 7403 6083 l 7400 6043 l 7397 6004 l 7393 5966 l 7389 5928 l 7385 5891 l 7381 5855 l 7377 5819 l 7372 5784 l 7368 5749 l 7363 5715 l 7357 5677 l 7350 5639 l 7344 5602 l 7337 5564 l 7329 5527 l 7321 5490 l 7313 5453 l 7305 5415 l 7296 5378 l 7287 5341 l 7277 5304 l 7267 5268 l 7257 5232 l 7247 5196 l 7236 5161 l 7226 5126 l 7215 5093 l 7204 5060 l 7194 5028 l 7183 4997 l 7172 4967 l 7162 4938 l 7151 4911 l 7141 4885 l 7131 4859 l 7121 4835 l 7112 4813 l 7103 4791 l 7094 4771 l 7085 4751 l 7076 4733 l 7068 4715 l 7053 4686 l 7039 4658 l 7024 4633 l 7011 4609 l 6997 4587 l 6983 4566 l 6970 4547 l 6957 4529 l 6945 4513 l 6933 4498 l 6921 4485 l 6911 4472 l 6901 4461 l 6891 4451 l 6883 4442 l 6875 4434 l 6867 4426 l 6860 4418 l 6850 4405 l 6840 4393 l 6831 4379 l 6822 4365 l 6813 4351 l 6805 4336 l 6796 4322 l 6788 4308 l 6781 4296 l 6774 4284 l 6767 4273 l 6760 4263 l 6753 4253 l 6746 4244 l 6738 4235 l 6729 4227 l 6720 4220 l 6711 4213 l 6701 4207 l 6691 4202 l 6681 4198 l 6672 4195 l 6662 4194 l 6653 4193 l 6643 4192 l 6632 4193 l 6621 4195 l 6609 4197 l 6597 4201 l 6584 4205 l 6571 4210 l 6558 4216 l 6545 4223 l 6533 4230 l 6522 4237 l 6510 4245 l 6498 4253 l 6487 4262 l 6475 4272 l 6463 4283 l 6450 4294 l 6438 4305 l 6427 4316 l 6416 4327 l 6407 4338 l 6399 4348 l 6391 4357 l 6385 4365 l 6377 4377 l 6371 4387 l 6367 4398 l 6363 4408 l 6361 4416 l 6359 4424 l 6358 4431 l 6358 4438 l 6356 4445 l 6354 4454 l 6351 4465 l 6348 4476 l 6345 4484 l 6345 4485 l gs col0 s gr % Polyline n 615 6180 m 616 6181 l 619 6184 l 627 6191 l 638 6201 l 651 6212 l 663 6222 l 675 6231 l 685 6238 l 696 6244 l 708 6250 l 718 6255 l 729 6259 l 741 6264 l 754 6268 l 769 6273 l 784 6278 l 800 6283 l 817 6289 l 833 6294 l 850 6299 l 866 6304 l 883 6310 l 897 6315 l 912 6320 l 928 6326 l 944 6332 l 962 6338 l 980 6343 l 998 6349 l 1016 6354 l 1034 6359 l 1052 6363 l 1068 6366 l 1085 6368 l 1100 6370 l 1115 6370 l 1130 6370 l 1144 6368 l 1159 6366 l 1175 6362 l 1190 6358 l 1206 6353 l 1222 6347 l 1238 6341 l 1253 6334 l 1268 6327 l 1283 6320 l 1297 6312 l 1311 6305 l 1325 6298 l 1339 6290 l 1353 6282 l 1368 6274 l 1383 6266 l 1399 6257 l 1416 6247 l 1433 6237 l 1449 6227 l 1466 6216 l 1482 6206 l 1497 6195 l 1512 6184 l 1526 6174 l 1540 6163 l 1552 6152 l 1564 6142 l 1576 6131 l 1589 6119 l 1602 6107 l 1615 6095 l 1629 6082 l 1643 6070 l 1656 6057 l 1670 6045 l 1683 6034 l 1696 6023 l 1709 6013 l 1721 6004 l 1733 5995 l 1745 5988 l 1757 5981 l 1769 5974 l 1782 5968 l 1795 5963 l 1809 5959 l 1823 5955 l 1837 5952 l 1851 5950 l 1865 5948 l 1878 5948 l 1891 5948 l 1904 5950 l 1916 5952 l 1927 5955 l 1937 5958 l 1948 5963 l 1959 5968 l 1969 5975 l 1980 5984 l 1991 5993 l 2002 6003 l 2012 6014 l 2023 6025 l 2033 6037 l 2043 6049 l 2053 6061 l 2062 6072 l 2071 6083 l 2079 6093 l 2088 6103 l 2096 6112 l 2105 6120 l 2114 6129 l 2124 6138 l 2134 6146 l 2146 6154 l 2158 6163 l 2170 6170 l 2183 6178 l 2197 6185 l 2211 6192 l 2225 6198 l 2240 6204 l 2255 6210 l 2269 6215 l 2284 6220 l 2300 6226 l 2318 6231 l 2336 6236 l 2355 6241 l 2375 6246 l 2395 6250 l 2416 6254 l 2437 6258 l 2457 6261 l 2477 6263 l 2496 6264 l 2515 6265 l 2533 6265 l 2550 6265 l 2567 6264 l 2584 6262 l 2601 6259 l 2619 6255 l 2637 6251 l 2655 6245 l 2673 6239 l 2691 6232 l 2709 6224 l 2727 6216 l 2744 6207 l 2761 6198 l 2778 6188 l 2794 6178 l 2810 6168 l 2825 6158 l 2839 6148 l 2853 6138 l 2867 6127 l 2882 6116 l 2898 6104 l 2914 6091 l 2930 6079 l 2946 6066 l 2963 6053 l 2980 6040 l 2997 6027 l 3013 6014 l 3029 6002 l 3045 5991 l 3061 5980 l 3076 5969 l 3090 5959 l 3105 5950 l 3121 5940 l 3138 5930 l 3155 5921 l 3173 5912 l 3191 5903 l 3210 5895 l 3229 5888 l 3248 5881 l 3268 5875 l 3287 5870 l 3306 5866 l 3325 5862 l 3343 5860 l 3360 5858 l 3378 5857 l 3395 5858 l 3412 5858 l 3430 5860 l 3448 5862 l 3467 5866 l 3486 5870 l 3505 5875 l 3525 5880 l 3544 5887 l 3563 5894 l 3582 5902 l 3600 5910 l 3617 5918 l 3633 5926 l 3648 5935 l 3662 5944 l 3675 5953 l 3689 5963 l 3703 5974 l 3717 5986 l 3730 5998 l 3743 6011 l 3756 6024 l 3769 6038 l 3781 6051 l 3793 6064 l 3804 6077 l 3815 6089 l 3825 6101 l 3835 6112 l 3845 6123 l 3855 6133 l 3865 6143 l 3876 6153 l 3887 6163 l 3899 6173 l 3912 6182 l 3924 6192 l 3937 6201 l 3950 6210 l 3963 6218 l 3976 6225 l 3988 6232 l 4000 6239 l 4013 6245 l 4025 6251 l 4038 6256 l 4051 6262 l 4065 6267 l 4080 6272 l 4095 6277 l 4110 6282 l 4125 6287 l 4139 6291 l 4154 6294 l 4168 6298 l 4181 6300 l 4193 6303 l 4205 6305 l 4215 6307 l 4226 6308 l 4237 6309 l 4248 6310 l 4261 6310 l 4275 6311 l 4290 6310 l 4307 6309 l 4325 6308 l 4344 6306 l 4365 6304 l 4388 6301 l 4412 6298 l 4438 6294 l 4465 6290 l 4495 6285 l 4515 6282 l 4535 6278 l 4557 6274 l 4580 6270 l 4604 6266 l 4630 6261 l 4656 6256 l 4684 6251 l 4713 6245 l 4742 6239 l 4772 6233 l 4803 6226 l 4833 6220 l 4864 6213 l 4895 6206 l 4926 6199 l 4956 6192 l 4986 6185 l 5015 6177 l 5043 6170 l 5070 6163 l 5096 6156 l 5121 6149 l 5145 6142 l 5168 6135 l 5190 6128 l 5218 6118 l 5244 6109 l 5270 6099 l 5294 6089 l 5318 6079 l 5342 6068 l 5364 6057 l 5386 6046 l 5407 6035 l 5427 6025 l 5446 6014 l 5464 6003 l 5481 5993 l 5497 5983 l 5512 5973 l 5526 5964 l 5538 5956 l 5550 5948 l 5562 5940 l 5573 5933 l 5587 5922 l 5602 5913 l 5617 5904 l 5632 5894 l 5648 5886 l 5664 5877 l 5681 5870 l 5697 5862 l 5715 5855 l 5732 5849 l 5750 5844 l 5768 5839 l 5786 5834 l 5805 5830 l 5821 5827 l 5837 5824 l 5855 5822 l 5873 5819 l 5892 5817 l 5913 5816 l 5933 5815 l 5954 5815 l 5976 5815 l 5997 5816 l 6018 5817 l 6038 5819 l 6057 5823 l 6075 5826 l 6093 5831 l 6109 5837 l 6124 5843 l 6138 5850 l 6152 5859 l 6165 5870 l 6178 5883 l 6190 5898 l 6201 5916 l 6213 5937 l 6224 5960 l 6236 5987 l 6247 6014 l 6258 6042 l 6267 6068 l 6275 6090 l 6280 6106 l 6284 6115 l 6285 6119 l 6285 6120 l gs col0 s gr % Polyline n 600 2700 m 601 2700 l 606 2701 l 616 2703 l 629 2704 l 642 2705 l 654 2705 l 665 2705 l 678 2703 l 688 2700 l 700 2697 l 714 2694 l 729 2691 l 744 2688 l 760 2685 l 776 2684 l 791 2684 l 806 2685 l 820 2688 l 831 2691 l 843 2696 l 854 2702 l 866 2710 l 878 2719 l 889 2729 l 900 2740 l 910 2752 l 919 2764 l 927 2777 l 934 2790 l 940 2803 l 945 2814 l 949 2826 l 953 2839 l 957 2852 l 960 2867 l 964 2881 l 968 2896 l 971 2912 l 975 2927 l 978 2942 l 982 2956 l 986 2971 l 990 2984 l 995 2998 l 1000 3011 l 1006 3024 l 1013 3038 l 1020 3052 l 1028 3066 l 1037 3081 l 1046 3095 l 1056 3109 l 1066 3122 l 1076 3135 l 1086 3147 l 1095 3158 l 1105 3168 l 1115 3178 l 1125 3187 l 1135 3195 l 1146 3204 l 1158 3213 l 1170 3221 l 1183 3229 l 1197 3238 l 1212 3245 l 1227 3253 l 1242 3260 l 1257 3267 l 1273 3273 l 1289 3279 l 1305 3285 l 1320 3290 l 1336 3295 l 1352 3301 l 1370 3306 l 1389 3312 l 1408 3317 l 1428 3323 l 1449 3328 l 1469 3333 l 1489 3338 l 1509 3343 l 1528 3347 l 1547 3351 l 1564 3354 l 1581 3357 l 1598 3360 l 1615 3363 l 1633 3365 l 1651 3367 l 1669 3369 l 1687 3370 l 1705 3370 l 1723 3370 l 1741 3369 l 1758 3368 l 1775 3366 l 1791 3363 l 1807 3360 l 1822 3357 l 1838 3353 l 1853 3348 l 1869 3342 l 1885 3336 l 1902 3330 l 1919 3322 l 1936 3315 l 1952 3307 l 1968 3299 l 1984 3291 l 1998 3283 l 2010 3276 l 2022 3269 l 2032 3263 l 2040 3258 l 2045 3254 l 2050 3250 l 2054 3247 l 2058 3244 l 2061 3240 l 2063 3237 l 2065 3234 l 2067 3231 l 2068 3228 l 2068 3224 l 2068 3221 l 2067 3218 l 2066 3214 l 2065 3211 l 2063 3207 l 2060 3204 l 2058 3200 l 2054 3196 l 2051 3192 l 2048 3188 l 2041 3180 l 2033 3171 l 2025 3161 l 2015 3150 l 2005 3138 l 1995 3126 l 1984 3114 l 1974 3101 l 1964 3089 l 1955 3078 l 1947 3068 l 1940 3058 l 1932 3046 l 1925 3035 l 1919 3023 l 1914 3012 l 1909 3000 l 1905 2988 l 1902 2977 l 1900 2965 l 1898 2954 l 1898 2943 l 1897 2930 l 1897 2917 l 1898 2903 l 1899 2889 l 1902 2874 l 1906 2859 l 1910 2845 l 1916 2832 l 1922 2820 l 1930 2810 l 1937 2802 l 1946 2795 l 1956 2789 l 1967 2782 l 1979 2777 l 1993 2772 l 2007 2767 l 2022 2764 l 2037 2761 l 2052 2758 l 2067 2756 l 2083 2755 l 2096 2754 l 2110 2754 l 2125 2754 l 2141 2754 l 2157 2755 l 2175 2757 l 2192 2759 l 2211 2763 l 2229 2767 l 2247 2772 l 2264 2778 l 2281 2784 l 2298 2792 l 2315 2800 l 2328 2807 l 2341 2815 l 2355 2824 l 2369 2833 l 2383 2844 l 2398 2855 l 2413 2866 l 2429 2879 l 2444 2891 l 2460 2904 l 2475 2917 l 2490 2930 l 2504 2943 l 2518 2956 l 2532 2968 l 2545 2980 l 2558 2991 l 2570 3003 l 2582 3013 l 2594 3024 l 2607 3035 l 2620 3046 l 2633 3057 l 2647 3069 l 2662 3080 l 2678 3091 l 2694 3102 l 2710 3112 l 2728 3122 l 2745 3132 l 2763 3142 l 2782 3151 l 2801 3159 l 2821 3167 l 2841 3175 l 2863 3183 l 2881 3188 l 2900 3194 l 2920 3200 l 2941 3205 l 2964 3211 l 2987 3216 l 3012 3222 l 3038 3227 l 3064 3232 l 3091 3236 l 3119 3241 l 3147 3245 l 3175 3249 l 3202 3252 l 3230 3255 l 3257 3258 l 3284 3260 l 3310 3262 l 3335 3263 l 3360 3264 l 3384 3265 l 3408 3265 l 3433 3265 l 3459 3264 l 3484 3263 l 3510 3261 l 3536 3259 l 3562 3256 l 3588 3253 l 3614 3249 l 3640 3244 l 3665 3240 l 3690 3234 l 3714 3228 l 3738 3222 l 3760 3216 l 3781 3209 l 3802 3202 l 3821 3195 l 3839 3188 l 3856 3180 l 3873 3173 l 3888 3164 l 3904 3156 l 3919 3147 l 3935 3138 l 3951 3128 l 3967 3118 l 3983 3107 l 3999 3096 l 4016 3085 l 4033 3073 l 4051 3061 l 4069 3049 l 4087 3038 l 4106 3026 l 4124 3015 l 4143 3004 l 4163 2993 l 4183 2983 l 4204 2973 l 4225 2963 l 4244 2954 l 4263 2946 l 4284 2938 l 4305 2929 l 4328 2921 l 4351 2913 l 4376 2904 l 4401 2896 l 4427 2888 l 4453 2879 l 4480 2871 l 4506 2863 l 4533 2856 l 4560 2848 l 4586 2841 l 4611 2835 l 4636 2828 l 4660 2822 l 4683 2817 l 4705 2812 l 4726 2807 l 4746 2803 l 4765 2799 l 4783 2795 l 4808 2790 l 4832 2786 l 4854 2783 l 4876 2780 l 4897 2778 l 4917 2776 l 4936 2775 l 4954 2775 l 4970 2776 l 4986 2777 l 5001 2779 l 5015 2781 l 5028 2784 l 5041 2787 l 5053 2791 l 5065 2795 l 5079 2800 l 5093 2806 l 5108 2813 l 5124 2820 l 5141 2828 l 5157 2836 l 5174 2845 l 5191 2855 l 5208 2864 l 5224 2874 l 5239 2883 l 5253 2892 l 5267 2901 l 5280 2910 l 5293 2919 l 5305 2928 l 5318 2937 l 5331 2947 l 5344 2957 l 5357 2968 l 5370 2979 l 5384 2990 l 5397 3001 l 5410 3012 l 5424 3023 l 5437 3034 l 5449 3044 l 5463 3055 l 5474 3065 l 5487 3074 l 5500 3085 l 5513 3095 l 5527 3106 l 5542 3117 l 5557 3127 l 5573 3138 l 5588 3148 l 5604 3158 l 5618 3167 l 5633 3175 l 5647 3182 l 5660 3188 l 5673 3193 l 5685 3198 l 5699 3201 l 5712 3204 l 5726 3206 l 5740 3206 l 5754 3206 l 5769 3204 l 5784 3202 l 5800 3198 l 5815 3194 l 5830 3188 l 5846 3183 l 5861 3176 l 5877 3170 l 5893 3163 l 5907 3156 l 5922 3149 l 5938 3141 l 5955 3133 l 5973 3124 l 5991 3115 l 6009 3105 l 6028 3095 l 6046 3085 l 6064 3074 l 6081 3064 l 6097 3054 l 6112 3044 l 6126 3034 l 6138 3024 l 6150 3015 l 6164 3002 l 6177 2989 l 6189 2976 l 6200 2963 l 6209 2949 l 6218 2936 l 6226 2923 l 6232 2911 l 6238 2900 l 6242 2891 l 6246 2882 l 6250 2875 l 6257 2863 l 6263 2854 l 6271 2846 l 6279 2839 l 6284 2836 l 6285 2835 l gs col0 s gr % Polyline 1 slj 7.500 slw gs clippath 5651 2696 m 5702 2728 l 5802 2572 l 5696 2683 l 5751 2540 l cp eoclip n 5685 2700 m 6735 1065 l 6735 1035 l gs col0 s gr gr % arrowhead 0 slj n 5751 2540 m 5696 2683 l 5802 2572 l 5760 2582 l 5751 2540 l cp gs 0.00 setgray ef gr col0 s % Polyline 1 slj gs clippath 6764 7919 m 6717 7956 l 6830 8102 l 6762 7966 l 6877 8065 l cp eoclip n 6750 7950 m 7800 9300 l gs col0 s gr gr % arrowhead 0 slj n 6877 8065 m 6762 7966 l 6830 8102 l 6835 8060 l 6877 8065 l cp gs 0.00 setgray ef gr col0 s % Polyline 1 slj gs clippath 3630 3735 m 3570 3735 l 3570 3920 l 3600 3770 l 3630 3920 l cp eoclip n 3600 3750 m 3600 4500 l gs col0 s gr gr % arrowhead 0 slj n 3630 3920 m 3600 3770 l 3570 3920 l 3600 3890 l 3630 3920 l cp gs 0.00 setgray ef gr col0 s % Polyline 1 slj gs clippath -327 4219 m -267 4209 l -297 4027 l -302 4180 l -356 4036 l cp eoclip n -600 2400 m -300 4200 l gs col0 s gr gr % arrowhead 0 slj n -356 4036 m -302 4180 l -297 4027 l -321 4061 l -356 4036 l cp gs 0.00 setgray ef gr col0 s % Polyline 1 slj gs clippath 14093 3267 m 14077 3324 l 14254 3375 l 14119 3305 l 14271 3317 l cp eoclip n 14100 3300 m 16200 3900 l gs col0 s gr gr % arrowhead 0 slj n 14271 3317 m 14119 3305 l 14254 3375 l 14234 3337 l 14271 3317 l cp gs 0.00 setgray ef gr col0 s % Polyline 1 slj gs clippath 14070 5684 m 14105 5733 l 14255 5625 l 14116 5688 l 14220 5576 l cp eoclip n 14100 5700 m 16200 4200 l gs col0 s gr gr % arrowhead 0 slj n 14220 5576 m 14116 5688 l 14255 5625 l 14213 5618 l 14220 5576 l cp gs 0.00 setgray ef gr col0 s $F2psEnd rs %%EndDocument endTexFig 1204 1956 a FD(Figure)28 b(6.)38 b FE(Decomp)r(osition)26 b(in)n(to)g(con)n(tours.)1944 1709 y Fh(C)1330 1355 y FE(in)n(t\(\000)1500 1322 y Fl(\000)1500 1374 y Fm(1)1551 1355 y FE(\))1093 410 y(ext\(\000)1276 377 y Fm(+)1276 429 y(1)1326 410 y FE(\))1092 812 y FC(~)-37 b(n)1139 820 y Fm(1)1802 292 y FC(\015)1846 260 y Fm(1)p Fp(;)p Fm(+)3337 812 y FE(\000)3385 820 y Fm(2)3441 812 y FE(=)21 b(\(\000)3600 779 y Fm(+)3600 831 y(2)3651 812 y FC(;)13 b FE(\000)3733 779 y Fl(\000)3733 831 y Fm(2)3785 812 y FE(\))148 481 y(\000)196 489 y Fm(1)252 481 y FE(=)21 b(\(\000)411 448 y Fm(+)411 500 y(1)462 481 y FC(;)13 b FE(\000)544 448 y Fl(\000)544 500 y Fm(1)596 481 y FE(\))218 2201 y FA(W)-8 b(e)35 b(are)f(going)g(to)g(deriv)m(e)g(an)f (upp)s(er)f(b)s(ound)g(for)h(the)h(probabilit)m(y)e(of)h(the)h (con\014gurations)f(com-)118 2309 y(patible)c(with)g(a)i(giv)m(en)f (set)h(\(\000)1175 2270 y Fx(+)1175 2335 y(1)1234 2309 y Fv(;)15 b FA(\000)1331 2270 y Ft(\000)1331 2335 y Fx(1)1391 2309 y FA(\))605 2577 y Fv(\026)660 2538 y Fx(+)660 2606 y Fs(\014)s(;N)790 2577 y FA(\(\000)882 2538 y Fx(+)882 2603 y(1)941 2577 y Fv(;)g FA(\000)1038 2538 y Ft(\000)1038 2603 y Fx(1)1098 2577 y FA(\))25 b(=)1337 2515 y(1)p 1264 2556 192 4 v 1264 2645 a Fv(Z)1333 2607 y Fx(+)1326 2674 y Fs(\014)s(;N)1481 2577 y Fv(Z)1550 2538 y Fx(+)1543 2622 y(ext)q(\(\000)1710 2592 y Fm(+)1710 2643 y(1)1761 2622 y Fx(\))1867 2463 y Fs(`)1823 2490 y Fq(Y)1824 2686 y Fs(i)p Fx(=1)1955 2577 y Fv(Z)2024 2538 y Ft(\006)2017 2616 y Fx(\001)2076 2593 y Fp(i)2076 2639 y(N)2153 2577 y Fv(Z)2222 2538 y Ft(\000)2215 2622 y Fx(in)n(t)q(\(\000)2370 2592 y Fl(\000)2370 2643 y Fm(1)2422 2622 y Fx(\))2484 2577 y FA(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2867 2591 y Fx(1)2907 2577 y Fu(j)p FA(\))15 b Fv(;)118 2847 y FA(where)34 b(the)g(length)g(of)g(the)g(con)m(tour)h(\000)1486 2861 y Fx(1)1560 2847 y FA(outside)e(the)h(set)h Fu([)2244 2814 y Fs(`)2244 2873 y(i)p Fx(=1)2362 2847 y Fv(R)2432 2814 y Fs(i)2431 2874 y(N)2532 2847 y FA(is)f(denoted)g(b)m(y)g Fu(j)p FA(\000)3187 2861 y Fx(1)3227 2847 y Fu(j)p FA(.)52 b(The)33 b(last)118 2959 y(term)e(in)f(the)h(RHS)f(tak)m(es)j(in)m(to)e (accoun)m(t)h(the)f(in)m(teraction)g(across)h(\000)2513 2973 y Fx(1)2583 2959 y FA(outside)e(the)h(sets)h Fv(R)3303 2926 y Fs(i)3302 2986 y(N)3369 2959 y FA(.)42 b(Using)118 3067 y(the)31 b(spin)d(\015ip)h(symmetry)-8 b(,)30 b(w)m(e)h(see)g (that)411 3348 y Fv(\026)466 3309 y Fx(+)466 3377 y Fs(\014)s(;N)595 3348 y FA(\(\000)687 3309 y Fx(+)687 3374 y(1)747 3348 y Fv(;)15 b FA(\000)844 3309 y Ft(\000)844 3374 y Fx(1)903 3348 y FA(\))26 b(=)1069 3246 y Fv(Z)1138 3208 y Fx(+)1131 3291 y(ext)r(\(\000)1299 3261 y Fm(+)1299 3312 y(1)1350 3291 y Fx(\))1397 3178 y Fq(Q)1482 3204 y Fs(`)1482 3273 y(i)p Fx(=1)1616 3246 y Fv(Z)1685 3208 y Fx(+)1678 3285 y(\001)1737 3262 y Fp(i)1737 3308 y(N)1799 3246 y Fv(Z)1868 3208 y Fx(+)1861 3291 y(in)n(t)q(\(\000)2016 3261 y Fl(\000)2016 3312 y Fm(1)2069 3291 y Fx(\))p 1069 3327 1031 4 v 1489 3416 a Fv(Z)1558 3378 y Fx(+)1551 3445 y Fs(\014)s(;N)2140 3348 y FA(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2523 3362 y Fx(1)2563 3348 y Fu(j)p FA(\))2654 3165 y Fq(0)2654 3329 y(@)2777 3234 y Fs(`)2734 3261 y Fq(Y)2735 3457 y Fs(i)p Fx(=1)2875 3250 y Fv(Z)2944 3212 y Ft(\006)2937 3289 y Fx(\001)2996 3266 y Fp(i)2996 3312 y(N)p 2875 3327 183 4 v 2875 3416 a Fv(Z)2944 3378 y Fx(+)2937 3455 y(\001)2996 3432 y Fp(i)2996 3478 y(N)3068 3165 y Fq(1)3068 3329 y(A)3177 3348 y Fv(:)227 b FA(\(3.15\))118 3645 y(Let)287 3622 y(~)281 3645 y(\000)338 3659 y Fx(1)409 3645 y FA(b)s(e)30 b(the)h(set)g(of)g(spin)e(con\014gurations)h (deduced)g(from)h(the)g(ones)g(compatible)f(with)g(\(\000)3411 3607 y Fx(+)3411 3671 y(1)3470 3645 y Fv(;)15 b FA(\000)3567 3607 y Ft(\000)3567 3671 y Fx(1)3626 3645 y FA(\))118 3758 y(b)m(y)30 b(\015ipping)e(the)i(spins)f(inside)f(in)m(t)o(\(\000) 1416 3720 y Ft(\000)1416 3784 y Fx(1)1475 3758 y FA(\))q(.)40 b(Equation)30 b(\(3.15\))j(can)d(b)s(e)g(rewritten)g(as)g(follo)m(ws) 760 4044 y Fv(\026)815 4005 y Fx(+)815 4073 y Fs(\014)s(;N)945 4044 y FA(\(\000)1037 4005 y Fx(+)1037 4070 y(1)1096 4044 y Fv(;)15 b FA(\000)1193 4005 y Ft(\000)1193 4070 y Fx(1)1252 4044 y FA(\))26 b(=)f Fv(\026)1464 4005 y Fx(+)1464 4073 y Fs(\014)s(;N)1594 4044 y FA(\()1635 4021 y(~)1629 4044 y(\000)1686 4058 y Fx(1)1725 4044 y FA(\))31 b(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2174 4058 y Fx(1)2214 4044 y Fu(j)p FA(\))2305 3861 y Fq(0)2305 4025 y(@)2428 3930 y Fs(`)2384 3957 y Fq(Y)2385 4153 y Fs(i)p Fx(=1)2525 3946 y Fv(Z)2594 3908 y Ft(\006)2587 3985 y Fx(\001)2646 3962 y Fp(i)2646 4008 y(N)p 2525 4023 V 2525 4112 a Fv(Z)2594 4074 y Fx(+)2587 4151 y(\001)2646 4128 y Fp(i)2646 4174 y(N)2718 3861 y Fq(1)2718 4025 y(A)2828 4044 y Fv(:)218 4321 y FA(By)30 b(the)h(de\014nition)d(of)j (the)f(surface)g(tension,)g(the)h(last)f(term)h(in)e(the)h(RHS)g(is)f (b)s(ounded)g(b)m(y)722 4474 y Fs(`)678 4502 y Fq(Y)679 4697 y Fs(i)p Fx(=1)819 4490 y Fv(Z)888 4452 y Ft(\006)881 4529 y Fx(\001)940 4506 y Fp(i)940 4552 y(N)p 819 4567 V 819 4656 a Fv(Z)888 4618 y Fx(+)881 4695 y(\001)940 4672 y Fp(i)940 4718 y(N)1037 4588 y Fr(6)40 b FA(exp)1302 4432 y Fq( )1374 4588 y Fu(\000)p Fv(N)1528 4550 y Fs(d)p Ft(\000)p Fx(1)1674 4432 y Fq(")1778 4474 y Fs(`)1727 4502 y Fq(X)1735 4697 y Fs(i)p Fx(=1)1873 4464 y Fq(Z)1938 4654 y Fk(b)1924 4670 y Fs(B)1977 4680 y Fp(i)2023 4588 y Fv(\034)2063 4603 y Fs(\014)2110 4588 y FA(\()n Fv(~)-43 b(n)2200 4602 y Fs(i)2228 4588 y FA(\))15 b Fv(d)p Fu(H)2402 4602 y Fs(x)2466 4588 y FA(+)20 b Fv(o)p FA(\()p Fv(N)10 b FA(\))2754 4432 y Fq(#)q(!)2910 4588 y Fv(:)494 b FA(\(3.16\))118 4860 y(Notice)31 b(that)g(in)e(the)i(particular)d(case)j(of)g(the)f (Ising)f(mo)s(del,)h(the)g(error)g(term)g Fv(o)p FA(\()p Fv(N)10 b FA(\))31 b(do)s(es)f(not)h(exists)118 4968 y(\(FK)m(G)h(prop)s(ert)m(y\).)218 5184 y(It)e(remains)f(to)i(c)m(hec)m (k)h(that)1104 5270 y Fq(X)1037 5483 y Fx(\(\000)1108 5453 y Fm(+)1108 5504 y(1)1160 5483 y Fs(;)p Fx(\000)1224 5453 y Fl(\000)1224 5504 y Fm(1)1275 5483 y Fx(\))1318 5356 y Fv(\026)1373 5318 y Fx(+)1373 5386 y Fs(\014)s(;N)1503 5356 y FA(\()1544 5334 y(~)1538 5356 y(\000)1595 5370 y Fx(1)1634 5356 y FA(\))f(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2083 5370 y Fx(1)2123 5356 y Fu(j)p FA(\))25 b Fr(6)g Fv(C)7 b FA(\()p Fv(\014)e FA(\))2502 5319 y Fs(`)2551 5356 y Fv(;)853 b FA(\(3.17\))p eop %%Page: 19 19 19 18 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(19)118 366 y FA(where)39 b(the)h(summation)f(is)f (tak)m(en)j(o)m(v)m(er)g(the)f(couples)f(\(\000)2183 328 y Fx(+)2183 393 y(1)2242 366 y Fv(;)15 b FA(\000)2339 328 y Ft(\000)2339 393 y Fx(1)2399 366 y FA(\))40 b(compatible)f(with)f (the)i(previous)118 485 y(construction.)78 b(As)42 b(the)h(spin)e (\015ip)g(corresp)s(ondence)h(\(\000)2140 446 y Fx(+)2140 511 y(1)2199 485 y Fv(;)15 b FA(\000)2296 446 y Ft(\000)2296 511 y Fx(1)2356 485 y FA(\))46 b Fu(\))2579 462 y FA(~)2574 485 y(\000)2631 499 y Fx(1)2712 485 y FA(is)c(not)h(a)g(one-to-one)i (the)118 592 y(ev)-5 b(aluation)30 b(of)38 b(\(3.17\))32 b(requires)d(some)i(care.)218 700 y(First)36 b(w)m(e)h(consider)f(the)h (restriction)f(of)i(the)f(spins)e(con\014gurations)h(in)f(eac)m(h)k Fv(R)3048 667 y Fs(i)3047 727 y(N)3114 700 y FA(,)g(in)c(this)h(case,) 118 808 y(the)j(corresp)s(ondence)f(is)g(a)h(one-to-one)h(b)s(ecause)f (the)g(spin)e(\015ip)f(o)s(ccurs)j(in)e(regions)h(delimited)e(b)m(y)118 916 y Fv(\015)170 883 y Fs(i;)p Fx(+)273 916 y Fv(;)15 b(\015)365 883 y Fs(i;)p Ft(\000)498 916 y FA(whic)m(h)30 b(are)h(de\014ned)e(unam)m(biguously)-8 b(.)39 b(F)-8 b(or)31 b(a)g(\014xed)e(spin)g(con\014guration)h(in)f Fu([)3248 883 y Fs(`)3248 942 y(i)p Fx(=1)3366 916 y Fv(R)3436 883 y Fs(i)3435 943 y(N)3502 916 y FA(,)i(w)m(e)118 1028 y(sum)f(o)m(v)m(er)j(the)e(con)m(tours)h(\000)1089 1042 y Fx(1)1159 1028 y FA(attac)m(hed)h(to)f(the)g(b)s(o)m(xes)f Fv(R)2122 995 y Fs(i)2121 1055 y(N)2188 1028 y FA(.)43 b(In)31 b(this)f(case)i(the)f(P)m(eierls)g(argumen)m(t)g(is)118 1141 y(fully)23 b(e\013ectiv)m(e)k(:)38 b(b)m(y)25 b(construction)g (\000)1423 1155 y Fx(1)1488 1141 y FA(stems)g(from)g(the)g(b)s(oundary) f(of)h(the)h(b)s(o)m(xes)f Fv(R)3067 1108 y Fs(i)3066 1167 y(N)3158 1141 y FA(whic)m(h)f(means)118 1248 y(that)34 b(the)f(con)m(tour)h(is)e(lo)s(calized)g(in)f(space.)49 b(Therefore)33 b(the)g(term)g(in)m(v)m(olving)f Fu(j)p FA(\000)2941 1262 y Fx(1)2981 1248 y Fu(j)p FA(,)i(i.e.)48 b(the)33 b(area)h(of)118 1359 y(the)d(con)m(tour)g(outside)e Fu([)980 1326 y Fs(`)980 1384 y(i)p Fx(=1)1098 1359 y Fv(R)1168 1326 y Fs(i)1167 1386 y(N)1235 1359 y FA(,)h(is)g(summable.) 218 1472 y(More)d(precisely)-8 b(,)27 b(for)g(an)m(y)g Fv(\033)j FA(compatible)c(with)g(\(\000)1979 1434 y Fx(+)1979 1498 y(1)2038 1472 y Fv(;)15 b FA(\000)2135 1434 y Ft(\000)2135 1498 y Fx(1)2194 1472 y FA(\),)28 b(w)m(e)g(write)e Fv(\033)i Fr( )d FA(\(\000)2930 1434 y Fx(+)2930 1498 y(1)2990 1472 y Fv(;)15 b FA(\000)3087 1434 y Ft(\000)3087 1498 y Fx(1)3146 1472 y FA(\).)40 b(The)26 b(image)118 1586 y(of)i Fv(\033)i FA(b)m(y)e(the)f(previous)f(mapping)g(will)f(b)s(e)i (denoted)g(b)m(y)32 b(~)-49 b Fv(\033)s FA(.)39 b(Let)28 b Fu(R)2418 1600 y Fs(N)2511 1586 y FA(=)d Fu([)2668 1553 y Fs(`)2668 1611 y(i)p Fx(=1)2786 1586 y Fv(R)2856 1553 y Fs(i)2855 1613 y(N)2949 1586 y FA(and)i(set)h Fv(\033)3314 1600 y Ft(R)3374 1611 y Fp(N)3464 1586 y FA(\(resp)118 1694 y Fv(\033)170 1708 y Ft(R)230 1685 y Fp(c)230 1731 y(N)292 1694 y FA(\))33 b(the)h(restriction)d(of)j Fv(\033)i FA(on)c Fu(R)1357 1708 y Fs(N)1458 1694 y FA(\(resp)g Fu(R)1765 1661 y Fs(c)1765 1721 y(N)1832 1694 y FA(\).)49 b(F)-8 b(or)34 b(simplicit)m(y)-8 b(,)31 b Fv(\015)38 b FA(will)31 b(denote)i(the)g(restriction)118 1817 y(of)e(\(\000)314 1779 y Fx(+)314 1843 y(1)373 1817 y Fv(;)15 b FA(\000)470 1779 y Ft(\000)470 1843 y Fx(1)529 1817 y FA(\))31 b(on)f Fu(R)798 1831 y Fs(N)896 1817 y FA(and)f Fu(C)36 b FA(the)30 b(restriction)g(on)g Fu(R)1951 1784 y Fs(c)1951 1844 y(N)2018 1817 y FA(.)458 1950 y Fq(X)391 2163 y Fx(\(\000)462 2134 y Fm(+)462 2185 y(1)513 2163 y Fs(;)p Fx(\000)577 2134 y Fl(\000)577 2185 y Fm(1)629 2163 y Fx(\))823 2037 y Fv(\026)878 1998 y Fx(+)878 2066 y Fs(\014)s(;N)1007 2037 y FA(\()1048 2014 y(~)1042 2037 y(\000)1099 2051 y Fx(1)1139 2037 y FA(\))g(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)1587 2051 y Fx(1)1627 2037 y Fu(j)p FA(\))26 b(=)1876 1950 y Fq(X)1809 2163 y Fx(\(\000)1880 2134 y Fm(+)1880 2185 y(1)1931 2163 y Fs(;)p Fx(\000)1995 2134 y Fl(\000)1995 2185 y Fm(1)2047 2163 y Fx(\))2239 1950 y Fq(X)2115 2163 y Fs(\033)r Fd( )p Fx(\(\000)2299 2134 y Fm(+)2299 2185 y(1)2350 2163 y Fs(;)p Fx(\000)2414 2134 y Fl(\000)2414 2185 y Fm(1)2466 2163 y Fx(\))2509 2037 y Fv(\026)2564 1998 y Fx(+)2564 2066 y Fs(\014)s(;N)2693 2037 y FA(\()5 b(~)-50 b Fv(\033)t FA(\))31 b(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)3233 2051 y Fx(1)3272 2037 y Fu(j)p FA(\))15 b Fv(;)1030 2443 y Fr(6)1141 2356 y Fq(X)1186 2553 y Ft(C)1287 2233 y Fq(0)1287 2393 y(B)1287 2451 y(@)1434 2356 y(X)1367 2553 y Fs(\033)1407 2569 y Fl(R)1460 2552 y Fp(c)1460 2595 y(N)1522 2553 y Fd( )p Ft(C)1664 2356 y Fq(X)1709 2547 y Fs(\015)1893 2356 y Fq(X)1825 2547 y Fs(\033)1865 2558 y Fl(R)1918 2575 y Fp(N)1980 2547 y Fd( )p Fs(\015)2106 2443 y Fv(\026)2161 2404 y Fx(+)2161 2472 y Fs(\014)s(;N)2291 2443 y FA(\()5 b(~)-50 b Fv(\033)s FA(\))2416 2233 y Fq(1)2416 2393 y(C)2416 2451 y(A)2512 2443 y FA(exp)o(\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2894 2457 y Fx(1)2934 2443 y Fu(j)p FA(\))15 b Fv(:)118 2771 y FA(F)-8 b(rom)31 b(the)g(one-to-one)h(corresp)s(ondence)e(on)g Fu(R)1796 2785 y Fs(N)1246 2894 y Fq(X)1178 3091 y Fs(\033)1218 3107 y Fl(R)1271 3090 y Fp(c)1271 3133 y(N)1333 3091 y Fd( )p Ft(C)1475 2894 y Fq(X)1521 3085 y Fs(\015)1704 2894 y Fq(X)1637 3085 y Fs(\033)1677 3096 y Fl(R)1730 3113 y Fp(N)1792 3085 y Fd( )p Fs(\015)1918 2981 y Fv(\026)1973 2942 y Fx(+)1973 3010 y Fs(\014)s(;N)2102 2981 y FA(\()5 b(~)-50 b Fv(\033)t FA(\))25 b Fr(6)g FA(1)15 b Fv(:)118 3302 y FA(Th)m(us)789 3413 y Fq(X)721 3626 y Fx(\(\000)792 3596 y Fm(+)792 3647 y(1)844 3626 y Fs(;)p Fx(\000)908 3596 y Fl(\000)908 3647 y Fm(1)960 3626 y Fx(\))1153 3499 y Fv(\026)1208 3461 y Fx(+)1208 3528 y Fs(\014)s(;N)1338 3499 y FA(\()1379 3476 y(~)1373 3499 y(\000)1430 3513 y Fx(1)1469 3499 y FA(\))31 b(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)1918 3513 y Fx(1)1958 3499 y Fu(j)p FA(\))25 b Fr(6)2155 3413 y Fq(X)2200 3609 y Ft(C)2301 3499 y FA(exp\()p Fu(\000)p Fv(\014)5 b Fu(j)p FA(\000)2684 3513 y Fx(1)2724 3499 y Fu(j)p FA(\))26 b Fr(6)f Fv(C)2978 3461 y Fs(`)2971 3522 y(\014)3033 3499 y Fv(:)118 3816 y FA(The)30 b(last)f(b)s(ound)f(follo)m(ws)h(from)h(the)g(P)m(eierls)f (argumen)m(t)i(and)e(the)h(fact)h(that)g(the)f(con)m(tour)h Fu(C)k FA(can)30 b(b)s(e)118 3924 y(divided)e(in)h(at)i(most)g Fv(`)f FA(in)m(terfaces.)218 4120 y(If)35 b(the)g(con)m(tour)h(\000)868 4134 y Fx(1)943 4120 y FA(is)e(not)i(unique,)f(similar)e(estimates)i (can)h(b)s(e)f(p)s(erformed)f(for)h(eac)m(h)h(con)m(tour.)118 4228 y(Indeed,)g(up)d(to)j(a)g(com)m(binatorial)e(factor)i(denoted)f Fv(\013)2026 4243 y Fs(`)2059 4228 y FA(,)h(w)m(e)g(asso)s(ciate)g(to)f (eac)m(h)h(of)g(the)f Fv(k)j FA(con)m(tours)118 4336 y(the)f(regions)g Fv(R)667 4303 y Fs(i)666 4363 y(N)770 4336 y FA(it)g(will)d(cross.)61 b(Then)36 b(w)m(e)i(p)s(erform)d(the)j (estimates)f(indep)s(enden)m(tly)d(and)j(obtain)118 4450 y(an)32 b(upp)s(er)d(b)s(ound)h(dep)s(ending)f(only)i(on)g Fv(\014)37 b FA(and)31 b Fv(`)h FA(:)43 b Fv(\013)2017 4465 y Fs(`)2050 4450 y FA(\()p Fv(C)2150 4465 y Fs(\014)2197 4450 y FA(\))2232 4417 y Fs(`)2266 4450 y FA(.)h(After)32 b(renormalization,)f(this)f(factor)118 4558 y(v)-5 b(anishes)21 b(in)g(the)i(thermo)s(dynamic)e(limit.)36 b(Com)m(bining)20 b(this)i(\014nal)f(estimate)i(with)e(\(3.17\))r(,)k(w)m(e)e(deduce)118 4666 y(\(3.14\))r(.)1455 4995 y(4.)47 b Fz(Ka)n(c)33 b(Ising)h(model)218 5157 y FA(The)29 b(previous)g(strategy)i(will)d(b)s (e)h(adapted)h(to)h(deriv)m(e)f(the)g(phase)g(co)s(existence)h(in)e (the)h(Kac)h(Ising)118 5264 y(mo)s(del.)39 b(This)28 b(requires)g(to)j(set)f(up)e(a)i(m)m(ultiscale)f(analysis)f(where)h (the)h(spin)e(v)-5 b(ariables)28 b(are)i(replaced)118 5372 y(b)m(y)36 b(coarse)i(grained)d(v)-5 b(ariables.)57 b(The)36 b(pro)s(of)g(relies)f(hea)m(vily)g(on)i(the)f(mo)s(del-dep)s (enden)m(t)f(estimates)118 5480 y(deriv)m(ed)30 b(in)f([CaPr)o(,)i(BMP) q(].)p eop %%Page: 20 20 20 19 bop 118 45 a Fx(20)1460 b(T.)23 b(BODINEA)n(U)118 366 y FA(4.1.)47 b FF(Coarse)29 b(graining.)46 b FA(The)25 b(long)h(range)f(structure)h(of)f(the)h(Kac)g(Ising)e(mo)s(del)h(prev)m (en)m(ts)h(us)f(from)118 474 y(using)k(directly)g(the)i(coarse)g (grained)f(estimates)h(of)f(subsection)g(3.1.)218 582 y(In)k(a)h(\014rst)f(step,)i(the)f(system)g(is)e(renormalized)h(on)g(a) h(scale)g(prop)s(ortional)e(to)i(the)g(range)g(of)g(the)118 690 y(in)m(teraction)f Fv(\015)631 657 y Ft(\000)p Fx(1)726 690 y FA(.)52 b(On)33 b(this)h(scale,)h(the)g(renormalized)e(system)h (b)s(eha)m(v)m(es)h(as)f(an)g(Ising)g(mo)s(del)f(with)118 798 y(e\013ectiv)m(e)41 b(in)m(v)m(erse)f(temp)s(erature)f(prop)s (ortional)e(to)k Fv(\015)2021 765 y Ft(\000)p Fs(d)2116 798 y FA(.)68 b(Th)m(us,)41 b(these)f(estimates)g(enables)f(us)g(to)118 906 y(implemen)m(t)29 b(a)i(second)f(renormalization)f(similar)f(to)j (the)g(one)f(in)m(tro)s(duced)f(in)g(subsection)h(3.1.)218 1014 y(It)h(should)e(b)s(e)i(stressed)g(that)h(the)f(di\016cult)e (estimates)j(to)g(construct)g(this)e(coarse)i(graining)e(w)m(ere)118 1122 y(already)g(obtained)g(in)f([CaPr,)h(BMP)q(].)118 1338 y Fn(L)-5 b(evel)33 b(1.)p 118 1353 308 4 v 218 1446 a FA(W)-8 b(e)33 b(in)m(tro)s(duce)e(t)m(w)m(o)i(in)m(termediate)f (scales)g(dep)s(ending)d(on)j(the)g(range)h(of)f(in)m(teraction)g Fv(\015)3330 1413 y Ft(\000)p Fx(1)3452 1446 y FA(=)c(2)3596 1413 y Fs(g)3636 1446 y FA(.)118 1554 y(Let)41 b Fv(L)i FA(=)g(2)555 1521 y Ft(\000)p Fs(`)643 1554 y Fv(\015)695 1521 y Ft(\000)p Fx(1)832 1554 y FA(=)g(2)991 1521 y Fs(g)r Ft(\000)p Fs(`)1156 1554 y FA(and)d Fv(H)50 b FA(=)42 b(2)1627 1521 y Fs(h)1672 1554 y Fv(\015)1724 1521 y Ft(\000)p Fx(1)1862 1554 y FA(=)g(2)2020 1521 y Fs(g)r Fx(+)p Fs(h)2156 1554 y FA(,)i(where)c Fv(`;)15 b(h)44 b Fu(2)e Fy(N)7 b FA(.)78 b(In)40 b(the)h(follo)m(wing)f Fv(`)118 1662 y FA(will)32 b(b)s(e)j(\014xed)f(and)g Fv(\015)40 b FA(will)32 b(go)k(to)g(0)f(so)g(that)h(the)f(condition)e Fv(`)g Fr(6)f Fv(g)39 b FA(will)32 b(b)s(e)i(alw)m(a)m(ys)i (satis\014ed.)53 b(By)118 1770 y(construction)30 b(eac)m(h)i(b)s(o)m(x) e Fy(B)1072 1784 y Fs(H)1176 1770 y FA(is)f(partionned)g(in)m(to)i (smaller)e(b)s(o)m(xes)h Fy(B)2531 1784 y Fs(L)2589 1770 y FA(.)218 1923 y(The)h(a)m(v)m(eraged)j(magnetization)f(in)d(the)j(b)s (o)m(x)e Fy(B)1873 1937 y Fs(L)1931 1923 y FA(\()p Fv(x)p FA(\))i(cen)m(tered)g(in)d Fv(x)e Fu(2)g Fy(D)2784 1937 y Fs(N)s(;L)2953 1923 y FA(w)m(as)k(in)m(tro)s(duced)f(in)118 2031 y(\(2.7\))40 b(and)d(denoted)h(b)m(y)g Fu(M)1121 2045 y Fs(N)s(;L)1252 2031 y FA(\()p Fv(x)p FA(\).)64 b(Giv)m(en)38 b Fv(")g(>)g FA(0)g(and)g Fv(\015)43 b(>)37 b FA(0,)k(the)d(phase)f(lab)s(els)f Fv(\021)3235 1998 y Fs(")3232 2058 y(N)s(;H)3416 2031 y FA(at)j(the)118 2148 y(mesoscopic)26 b(scale)f Fv(H)32 b FA(are)26 b(de\014ned)e(as)h (follo)m(ws)g(:)38 b(the)25 b(b)s(o)m(x)g Fy(B)2192 2162 y Fs(H)2265 2148 y FA(\()p Fv(x)p FA(\))h(cen)m(tered)g(in)e Fv(x)h Fu(2)g Fy(D)3092 2162 y Fs(N)t(;H)3270 2148 y FA(is)f(lab)s(elled)118 2256 y(b)m(y)481 2487 y Fv(\021)529 2449 y Fs(")526 2509 y(N)s(;H)672 2487 y FA(\()p Fv(x)p FA(\))i(=)916 2331 y Fq(\()989 2424 y Fu(\006)p FA(1)p Fv(;)273 b FA(if)30 b Fu(jM)1621 2438 y Fs(N)s(;L)1752 2424 y FA(\()p Fv(y)s FA(\))21 b Fu(\007)f Fv(m)2062 2391 y Ft(\003)2062 2452 y Fs(\014)2109 2424 y Fu(j)25 b Fr(6)g Fv(";)107 b Fu(8)p Fy(B)2534 2438 y Fs(L)2592 2424 y FA(\()p Fv(y)s FA(\))26 b Fu(\032)f Fy(B)2886 2438 y Fs(H)2960 2424 y FA(\()p Fv(x)p FA(\))15 b Fv(;)989 2555 y FA(0)p Fv(;)344 b FA(otherwise)15 b Fv(:)118 2718 y FA(The)36 b(parameter)h Fv(")g FA(quan)m(ti\014es)f(the)h(deviation)f (of)h(the)f(a)m(v)m(eraged)j(magnetization)e(from)f(the)h(mean)118 2826 y(\014eld)29 b(magnetization)i Fv(m)986 2793 y Ft(\003)986 2853 y Fs(\014)1063 2826 y FA(\(and)f(not)h Fv(m)1517 2793 y Ft(\003)1517 2853 y Fs(\014)s(;\015)1654 2826 y FA(\(2.3\))r(\).)218 2989 y(F)-8 b(ollo)m(wing)30 b([CaPr,)i(BMP],)g (w)m(e)g(in)m(tro)s(duce)e(the)h(renormalized)f(notions)g(of)h(b)s(o)m (xes,)h(con)m(tours)g(and)118 3097 y(b)s(oundary)c(conditions)h(at)i (the)g(mesoscopic)g(scale)f Fv(H)7 b FA(.)334 3227 y Fu(\017)42 b FA(A)36 b(b)s(o)m(x)g Fy(B)759 3241 y Fs(H)833 3227 y FA(\()p Fv(x)p FA(\))g(is)f Fn(c)-5 b(orr)g(e)g(ct)38 b FA(if)d Fv(\021)1526 3194 y Fs(")1523 3254 y(N)s(;H)1669 3227 y FA(\()p Fv(x)p FA(\))h(=)e Fu(\006)p FA(1)i(and)f(if)g(all)g (the)h Fv(?)p FA(-neigh)m(b)s(oring)f(b)s(o)m(xes)h(ha)m(v)m(e)421 3344 y(the)30 b(same)h(lab)s(els)e(as)h Fy(B)1227 3358 y Fs(H)1300 3344 y FA(\()p Fv(x)p FA(\).)334 3452 y Fu(\017)42 b FA(The)c(supp)s(ort)f(of)i(a)g(con)m(tour)g(is)f(a)h(maximal)f Fv(?)p FA(-connected)i(comp)s(onen)m(t)f(of)g(the)g Fn(inc)-5 b(orr)g(e)g(ct)421 3560 y FA(b)s(o)m(xes.)54 b(A)35 b(con)m(tour)g(is)f (de\014ned)g(b)m(y)g(its)g(supp)s(ort)f(and)i(b)m(y)f(the)h(sp)s (eci\014cation)f(of)h(the)g(phase)421 3668 y(lab)s(els)28 b(on)j(the)f(supp)s(ort.)334 3776 y Fu(\017)42 b FA(Con)m(trary)31 b(to)h(the)g(lo)m(w)f(temp)s(erature)h(Ising)e(mo)s(del,)h(w)m(e)h(are) f(going)h(to)g(consider)e(b)s(oundary)421 3883 y(conditions)44 b(whic)m(h)g(are)h(only)g(statistically)f(pure.)85 b(A)45 b(region)g(\003)g(\(measurable)g(wrt)g(the)421 3991 y(partition)23 b(at)j(the)e(scale)h Fv(H)7 b FA(\))25 b(has)f(+)h(b)s(oundary)d (conditions)h(in)h(a)m(v)m(eraged)i(if)e(the)h(phase)f(lab)s(els)421 4120 y Fv(\021)469 4072 y Fs("=)p Fx(2)466 4149 y Fs(N)s(;H)636 4120 y FA(asso)s(ciated)h(to)h Fv(\033)1221 4134 y Fx(\003)1270 4115 y Fp(c)1330 4120 y FA(are)f(uniformly)c(equal)j(to)h(1.)40 b(This)22 b(set)j(of)g(b)s(oundary)d(conditions)h(is)421 4248 y(denoted)f(b)m(y)h Fv(G)946 4215 y Fx(+)p Fs(;")1058 4248 y FA(\(\003\))j Fu(\032)f FA([)p Fu(\000)p FA(1)p Fv(;)15 b FA(1])1564 4215 y Fx(\003)1613 4192 y Fp(c)1650 4248 y FA(.)38 b(In)22 b(the)h(same)g(w)m(a)m(y)-8 b(,)26 b(the)c(set)h(of)g Fu(\000)f FA(b)s(oundary)f(conditions)421 4356 y(in)29 b(a)m(v)m(eraged)j(is)e(denoted)g(b)m(y)h Fv(G)1536 4323 y Ft(\000)p Fs(;")1647 4356 y FA(\(\003\).)218 4487 y(F)-8 b(or)33 b(the)f(renormalized)f(con)m(tours,)j(a)f(P)m (eierls)e(estimate)i(of)g(the)f(t)m(yp)s(e)h(\(2.8\))h(has)e(b)s(een)g (pro)m(v)m(en)h(in)118 4595 y([CaPr])118 4762 y FF(Theorem)45 b(4.1.)i Fn(Ther)-5 b(e)41 b(exist)h(functions)f Fv(")1717 4729 y Ft(\003)1757 4762 y FA(\()p Fv(\014)5 b FA(\))41 b Fv(>)f FA(0)p Fn(,)k Fv(`)p FA(\()p Fv(\014)5 b(;)15 b(")p FA(\))42 b Fu(2)e Fy(N)7 b Fv(;)15 b(h)p FA(\()q Fv(\014)5 b(;)15 b(")q FA(\))47 b Fu(2)40 b Fy(N)6 b Fn(,)49 b Fv(c)p FA(\()p Fv(\014)5 b(;)15 b(")p FA(\))43 b Fv(>)d FA(0)p Fn(,)118 4870 y Fv(c)157 4837 y Ft(0)181 4870 y FA(\()p Fv(\014)5 b(;)15 b(")p FA(\))38 b Fv(>)e FA(0)j Fn(such)g(that)h(the)f(fol)5 b(lowing)40 b(holds.)61 b(L)-5 b(et)39 b Fv(\015)j(>)36 b FA(0)p Fv(;)15 b(\014)42 b(>)36 b FA(1)j Fn(and)h Fv(")d(<)f(")2998 4837 y Ft(\003)3037 4870 y Fn(.)60 b(Then)39 b(for)h(any)118 4978 y(r)-5 b(e)g(gion)36 b FA(\003)e Fn(\(me)-5 b(asur)g(able)37 b(wrt)e(the)g(p)-5 b(artition)36 b(on)f(the)g Fv(H)42 b Fn(sc)-5 b(ale\))35 b(and)g(any)g(gener)-5 b(alize)g(d)36 b(c)-5 b(ontour)36 b FA(\000)e Fn(in)118 5085 y FA(\003)480 5272 y Fu(8)p Fv(\033)583 5286 y Fx(\003)632 5267 y Fp(c)692 5272 y Fu(2)25 b Fv(G)849 5234 y Fx(+)p Fs(;")961 5272 y FA(\(\003\))p Fv(;)202 b(\026)1376 5287 y Fs(\014)s(;\015)t(;)p Fx(\003)1567 5198 y Fq(\000)1608 5272 y FA(\000)1680 5194 y Fq(\014)1680 5249 y(\014)1711 5272 y Fv(\033)1763 5286 y Fx(\003)1812 5267 y Fp(c)1848 5198 y Fq(\001)1930 5272 y Fr(6)25 b Fv(c)2065 5234 y Ft(0)2088 5272 y FA(\()p Fv(\014)5 b(;)15 b(")p FA(\))32 b(exp)2482 5143 y Fq(\022)2549 5272 y Fu(\000)2630 5210 y Fv(c)p FA(\()p Fv(\014)5 b(;)15 b(")p FA(\))p 2630 5251 250 4 v 2708 5334 a Fv(\015)2760 5308 y Fs(d)2904 5272 y Fu(j)p FA(\000)p Fu(j)3011 5143 y Fq(\023)3109 5272 y Fv(;)341 b FA(\(4.1\))118 5480 y Fn(wher)-5 b(e)34 b Fu(j)p FA(\000)p Fu(j)f Fn(denotes)g(the)g(numb) -5 b(er)33 b(of)g(b)-5 b(oxes)34 b(in)e(the)h(c)-5 b(ontour)34 b FA(\000)p Fn(.)p eop %%Page: 21 21 21 20 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(21)218 378 y FA(After)33 b(the)h(renormalization) e(pro)s(cedure,)h(the)h(e\013ectiv)m(e)h(temp)s(erature)e(b)s(ecomes) 3133 333 y Fs(c)p Fx(\()p Fs(\014)s(;")p Fx(\))p 3133 357 181 4 v 3185 414 a Fs(\015)3225 395 y Fp(d)3324 378 y FA(.)50 b(There-)118 499 y(fore,)33 b(for)e Fv(\015)37 b FA(small)30 b(enough,)i(the)g(coarse)h(grained)e(system)g(b)s(eha)m (v)m(es)i(as)f(an)f(Ising)g(mo)s(del)f(in)h(the)h(lo)m(w)118 607 y(temp)s(erature)e(regime.)218 714 y(A)c(more)f(precise)g (description)f(of)i(the)g(pure)f(phases)g(has)g(b)s(een)g(deriv)m(ed)g (in)f([BMP)q(])i(\(Theorem)g(2.4\))118 822 y(:)52 b(the)36 b(Gibbs)f(measures)h(with)e(almost)j(pure)e(b)s(oundary)f(conditions)g (relax)i(exp)s(onen)m(tially)e(fast)j(to)118 930 y(the)31 b(corresp)s(onding)d(pure)h(phase.)118 1101 y FF(Theorem)48 b(4.2.)h FA([BMP)q(])44 b Fn(F)-7 b(or)45 b(any)g Fv(\014)51 b(>)45 b FA(1)p Fn(,)i Fu(8)p Fv(")f Fu(2)p FA(]0)p Fv(;)15 b(")2148 1068 y Ft(\003)2188 1101 y FA(\()p Fv(\014)5 b FA(\)[)45 b Fn(ther)-5 b(e)45 b(exists)g Fv(\015)5 b FA(\()p Fv(\014)g(;)15 b(")p FA(\))47 b Fv(>)f FA(0)p Fv(;)15 b(c)p FA(\()p Fv(")p FA(\))48 b Fv(>)118 1211 y FA(0)g Fn(such)f(that)i(the)f(fol)5 b(lowing)48 b(holds.)88 b(F)-7 b(or)49 b(any)f(subset)f FA(\001)g Fn(of)h Fy(Z)2481 1178 y Fs(d)2517 1211 y Fn(,)j(for)d(any)g Fu(K)53 b(\032)f FA(\001)p Fn(,)f(one)c(has)118 1319 y Fu(8)p Fv(\015)30 b Fr(6)25 b Fv(\015)5 b FA(\()p Fv(\014)g(;)15 b(")p FA(\))p Fv(;)g Fu(8)p Fv(\033)745 1333 y Fx(\001)804 1314 y Fp(c)867 1319 y Fu(2)25 b Fv(G)1024 1286 y Fx(+)p Fs(;")1135 1319 y FA(\(\001\))611 1403 y Fq(\014)611 1458 y(\014)611 1512 y(\014)641 1508 y Fv(\026)696 1523 y Fs(\014)s(;\015)t(;)p Fx(\001)881 1434 y Fq(\000)923 1508 y Fv(\033)975 1522 y Ft(K)1033 1431 y Fq(\014)1033 1485 y(\014)1063 1508 y Fv(\033)1115 1522 y Fx(\001)1174 1503 y Fp(c)1210 1434 y Fq(\001)1272 1508 y Fu(\000)20 b Fv(\026)1418 1470 y Fx(+)1418 1537 y Fs(\014)s(;\015)1525 1508 y FA(\()p Fv(\033)1612 1522 y Ft(K)1670 1508 y FA(\))1705 1403 y Fq(\014)1705 1458 y(\014)1705 1512 y(\014)1761 1508 y Fr(6)25 b Fu(jK)q(j)42 b FA(exp)2173 1434 y Fq(\000)2235 1508 y Fu(\000)20 b Fv(c)15 b(\015)2432 1470 y Fx(2)2487 1508 y Fn(dist)q FA(\()p Fu(K)q Fv(;)g FA(\001)2850 1470 y Fs(c)2885 1508 y FA(\))2920 1434 y Fq(\001)2978 1508 y Fv(:)118 1754 y Fn(L)-5 b(evel)33 b(2.)p 118 1769 308 4 v 218 1862 a FA(The)e(previous)f(estimates)j(are)f(the)g(building)c (blo)s(c)m(ks)j(for)h(the)g(next)g(renormalization)f(step.)45 b(The)118 1970 y(phase)38 b(lab)s(els)f Fv(\021)691 1937 y Fs(")688 1997 y(N)s(;H)872 1970 y FA(quan)m(tify)h(only)g(the)g (deviations)g(of)g(the)h(a)m(v)m(eraged)h(magnetization)f(from)f Fv(m)3614 1937 y Ft(\003)3614 1998 y Fs(\014)118 2087 y FA(instead)30 b(of)i Fv(m)617 2054 y Ft(\003)617 2115 y Fs(\014)s(;\015)723 2087 y FA(.)43 b(F)-8 b(urthermore,)31 b(the)g(con)m(trol)h(of)f(these)g(deviations)f(\(4.1\))j(induces)c(a)j (dep)s(endency)118 2212 y(b)s(et)m(w)m(een)f(the)g(accuracy)g Fv(")g FA(and)f(the)g(range)h(of)f(the)h(in)m(teraction)f Fv(\015)2425 2179 y Ft(\000)p Fx(1)2520 2212 y FA(.)218 2320 y(By)c(analogy)g(with)f(Subsection)g(3.1,)j(w)m(e)e(will)e (de\014ne)h(a)h(coarse)h(graining)e(at)i(the)f(mesoscopic)g(scale)118 2428 y Fv(K)34 b Fu(\035)27 b Fv(H)7 b FA(.)44 b(The)31 b(phase)g(lab)s(els)e Fv(\021)1245 2395 y Fs(")1242 2455 y(N)s(;H)1420 2428 y FA(are)j(going)f(to)i(pla)m(y)e(the)g(role)g(of)h (the)g(spins.)42 b(This)29 b(will)g(enables)118 2539 y(us)36 b(to)i(strengthen)f(the)g(con)m(trol)g(on)g(the)g(deviation)f (of)h(the)g(magnetization)g(in)f Fv(K)7 b FA(-b)s(o)m(xes)37 b(from)f(its)118 2647 y(exp)s(ected)31 b(v)-5 b(alue)30 b Fv(m)812 2614 y Ft(\003)812 2675 y Fs(\014)s(;\015)949 2647 y FA(with)f(an)h(arbitrary)f(precision.)218 2863 y(F)-8 b(or)30 b Fv(\014)g(>)25 b FA(1,)30 b(the)g(parameters)f Fv(\015)5 b(;)15 b(";)g(L)30 b FA(and)f Fv(H)36 b FA(are)30 b(\014xed)e(suc)m(h)h(that)h(Theorems)f(4.1)h(and)e(4.2)j(hold)118 2971 y(and)j(that)h(the)f(e\013ectiv)m(e)i(temp)s(erature)e(is)f(lo)m (w)h(enough.)52 b(The)34 b(parameter)h Fv(\020)j(>)31 b FA(0)k(will)c(con)m(trol)k(the)118 3079 y(accuracy)d(of)e(the)h (coarse)g(graining)e(at)i(the)g(scale)f Fv(K)i FA(=)25 b(2)2117 3046 y Fs(k)2160 3079 y Fv(H)7 b FA(.)218 3194 y(Let)25 b Fv(x)f FA(b)s(e)g(in)677 3170 y Fq(b)669 3194 y Fy(D)729 3208 y Fs(N)s(;K)907 3194 y FA(and)g Fv(\013)h FA(b)s(e)f(in)f(\(0)p Fv(;)15 b FA(1\).)41 b(The)24 b(b)s(o)m(x)1999 3170 y Fq(b)1994 3194 y Fy(B)2049 3208 y Fs(N)s(;K)2202 3194 y FA(\()p Fv(x)p FA(\))h(is)e(+)i Fn(go)-5 b(o)g(d)26 b FA(if)e(the)g(spin)f(con\014guration)118 3308 y(inside)28 b(the)j(enlarged)f(b)s(o)m(x)g(of)g(side)g(length)g Fv(K)c FA(+)20 b(2)1874 3275 y Fs(\013k)1963 3308 y Fv(H)37 b FA(is)29 b(t)m(ypical,)i(i.e.)118 3416 y FF(\(P1\))f FA(The)f(b)s(o)m(x)h Fy(B)768 3430 y Fs(K)842 3416 y FA(\()p Fv(x)p FA(\))h(is)e(surrounded)e(b)m(y)j(a)g(surface)g(of)g(b)s (o)m(xes)g Fy(B)2476 3430 y Fs(H)2579 3416 y FA(in)f Fv(@)5 b Fy(B)2793 3430 y Fs(K)2867 3416 y FA(\()p Fv(x)p FA(\))30 b(with)f(mesoscopic)118 3524 y(phase)h(lab)s(els)f Fv(\021)675 3491 y Fs(")672 3551 y(N)s(;H)848 3524 y FA(uniformly)f(equal)h(to)j(1.)118 3640 y FF(\(P2\))26 b FA(The)e(a)m(v)m(eraged)k(magnetization)e Fu(M)1597 3654 y Fs(N)s(;K)1744 3640 y FA(\()p Fv(x)p FA(\))g(inside)d Fy(B)2200 3654 y Fs(K)2274 3640 y FA(\()p Fv(x)p FA(\))j(is)f(close)g (to)i(the)e(equilibrium)c(v)-5 b(alue)118 3748 y Fv(m)198 3715 y Ft(\003)198 3776 y Fs(\014)s(;\015)1417 3812 y Fq(\014)1417 3867 y(\014)1447 3890 y Fu(M)1556 3904 y Fs(N)s(;K)1704 3890 y FA(\()p Fv(x)p FA(\))20 b Fu(\000)g Fv(m)2017 3852 y Ft(\003)2017 3913 y Fs(\014)s(;\015)2124 3812 y Fq(\014)2124 3867 y(\014)2180 3890 y Fr(6)25 b Fv(\020)c(:)1113 b FA(\(4.2\))118 4032 y(The)30 b Fu(\000)g Fn(go)-5 b(o)g(d)32 b FA(b)s(o)m(xes)f(are)f(de\014ned)g(in)f(the)h (same)h(w)m(a)m(y)-8 b(.)218 4200 y(On)29 b(the)i(mesoscopic)f(lev)m (el,)h(eac)m(h)g(b)s(o)m(x)1608 4177 y Fq(b)1603 4200 y Fy(B)1657 4214 y Fs(N)s(;K)1810 4200 y FA(\()p Fv(x)p FA(\))g(is)f(lab)s(elled)e(b)m(y)i(a)h(mesoscopic)f(phase)g(lab)s(el) 663 4448 y Fu(8)p Fv(x)25 b Fu(2)884 4424 y Fq(b)877 4448 y Fy(D)937 4462 y Fs(N)s(;K)1090 4448 y Fv(;)197 b(u)1364 4403 y Fs(\020)1364 4476 y(N)s(;K)1511 4448 y FA(\()p Fv(x)p FA(\))26 b(=)1755 4292 y Fq(\()1828 4386 y Fu(\006)p FA(1)p Fv(;)273 b FA(if)2331 4363 y Fq(b)2326 4386 y Fy(B)2380 4400 y Fs(N)s(;K)2533 4386 y FA(\()p Fv(x)p FA(\))31 b(is)f Fu(\006)g Fn(go)-5 b(o)g(d)32 b Fv(;)1828 4516 y FA(0)p Fv(;)344 b FA(otherwise)p Fv(:)218 4686 y FA(The)30 b(t)m(ypical)g(b)s(eha)m(vior)f(follo)m(ws)h(from)118 4857 y FF(Theorem)37 b(4.3.)43 b Fn(L)-5 b(et)36 b Fv(\014)e(>)c FA(1)35 b Fn(and)h(\014x)f Fv(\015)1550 4872 y Fs(\014)1627 4857 y Fv(>)29 b FA(0)35 b Fn(and)h Fv(")30 b(>)f FA(0)35 b Fn(such)g(that)i(the)e(The)-5 b(or)g(ems)37 b(4.1)f(and)g(4.2)118 4964 y(ar)-5 b(e)40 b(satis\014e)-5 b(d.)62 b(F)-7 b(or)40 b(any)g Fv(\015)i(<)36 b(\015)5 b FA(\()p Fv(\014)g(;)15 b(")p FA(\))p Fn(,)42 b Fv(\020)i(>)36 b FA(0)p Fn(,)41 b(the)e(fol)5 b(lowing)40 b(holds)h(uniformly)f(for)g(domains)g FA(\003)118 5072 y Fn(\(me)-5 b(asur)g(able)35 b(wrt)e Fv(K)7 b Fn(-p)-5 b(artitions\))35 b(and)e(for)g(any)h Fv(\033)1892 5086 y Fx(\003)1941 5068 y Fp(c)2002 5072 y Fu(2)25 b Fv(G)2159 5039 y Fx(+)p Fs(;")2271 5072 y FA(\(\003\))329 5261 y Fu(8f)p Fv(x)477 5275 y Fx(1)516 5261 y Fv(;)15 b(:)g(:)g(:)i(;)e(x)770 5276 y Fs(`)803 5261 y Fu(g)p Fv(;)109 b(\026)1037 5276 y Fs(\014)s(;\015)t(;)p Fx(\003)1228 5160 y Fq(\020)1282 5261 y Fv(u)1334 5217 y Fs(\020)1334 5290 y(N)s(;K)1481 5261 y FA(\()p Fv(x)1568 5275 y Fx(1)1608 5261 y FA(\))25 b(=)g(0)p Fv(;)15 b(:)g(:)g(:)i(;)e(u) 2063 5217 y Fs(\020)2063 5290 y(N)s(;K)2211 5261 y FA(\()p Fv(x)2298 5276 y Fs(`)2331 5261 y FA(\))26 b(=)f(0)2548 5184 y Fq(\014)2548 5238 y(\014)2604 5261 y Fv(\033)2656 5275 y Fx(\003)2705 5256 y Fp(c)2741 5160 y Fq(\021)2836 5261 y Fr(6)2932 5187 y Fq(\000)2973 5261 y Fv(\032)3020 5217 y Fs(\020)3020 5290 y(\015)t(;K)3149 5187 y Fq(\001)3190 5210 y Fs(`)3238 5261 y Fv(;)212 b FA(\(4.3\))118 5472 y Fn(wher)-5 b(e)34 b(the)f(p)-5 b(ar)g(ameter)35 b Fv(\032)1000 5428 y Fs(\020)1000 5501 y(\015)t(;K)1161 5472 y Fn(vanishes)e(as)h Fv(K)39 b Fn(go)-5 b(es)33 b(to)g(in\014nity.)p eop %%Page: 22 22 22 21 bop 118 45 a Fx(22)1460 b(T.)23 b(BODINEA)n(U)218 366 y FA(The)42 b(pro)s(of)h(go)s(es)h(along)f(the)h(lines)d(of)j (Theorem)f(3.1;)51 b(the)43 b(P)m(eierls)f(argumen)m(t)i(is)e(implied)e (b)m(y)118 474 y(Theorem)30 b(4.1)i(and)d(the)i(deca)m(y)h(of)e (correlations)g(b)m(y)g(Theorem)g(4.2.)118 846 y(4.2.)47 b FF(Structure)d(of)h(the)f(pro)s(of.)i FA(As)39 b(explained)e(in)g (Section)i(3,)i(the)e(pro)s(of)f(of)h(Theorem)f(2.3)i(is)118 954 y(based)32 b(up)s(on)e(coarse)k(grained)d(estimates.)47 b(Therefore,)32 b(the)h(same)f(strategy)i(can)e(b)s(e)g(transp)s(osed)f (to)118 1062 y(the)37 b(Kac)g(Ising)f(mo)s(del)f(b)m(y)i(using)e(the)i (mesoscopic)g(represen)m(tation)g(describ)s(ed)e(ab)s(o)m(v)m(e.)61 b(The)36 b(\014rst)118 1170 y(part)24 b(of)g(the)g(pro)s(of)f(is)g(v)m (ery)h(similar)e(to)i(the)g(approac)m(h)g(in)m(tro)s(duced)f(in)f ([BBBP)r(,)i(BBP])g(and)g(therefore,)118 1278 y(w)m(e)34 b(do)f(not)h(rep)s(eat)f(the)h(argumen)m(ts)f(of)h(Section)f(3.)50 b(Nev)m(ertheless,)35 b(the)e(deriv)-5 b(ation)32 b(of)h(the)h(precise) 118 1386 y(surface)c(tension)g(factor)h(requires)e(further)g(analysis.) 218 1494 y(In)h(the)i(case)g(of)f(nearest)h(neigh)m(b)s(or)e(Ising)g (mo)s(del)g(at)i(lo)m(w)f(temp)s(erature,)g(the)h(lo)s(calization)e(of) h(the)118 1602 y(in)m(terface)c(at)g(the)f(mesoscopic)g(lev)m(el)g(b)m (y)g(the)g(minimal)e(section)i(argumen)m(t)g(implied)d(directly)-8 b(,)27 b(thanks)118 1710 y(to)39 b(the)g(coarse)h(graining,)f(the)g(lo) s(calization)e(at)i(the)g(microscopic)f(lev)m(el.)65 b(Therefore)38 b(the)h(ratio)f(of)118 1827 y(partition)27 b(functions)894 1791 y Fs(Z)947 1767 y Fl(\006)p 894 1806 105 4 v 895 1860 a Fs(Z)948 1841 y Fm(+)1036 1827 y FA(\(see)i(\(3.9\))h(or)e(\(3.16\))r(\))g(arises)f(from)h(the)g(v)m (ery)g(construction)f(of)h(the)g(coarse)118 1935 y(graining.)60 b(This)36 b(is)g(no)h(longer)g(the)h(case,)i(b)s(oth)d(for)g(the)g(lo)m (w)m(er)h(and)f(the)g(upp)s(er)e(b)s(ound.)60 b(Indeed,)118 2043 y(the)39 b(lo)s(calization)e(at)i(the)f(scale)h Fv(K)45 b FA(implies)35 b(only)j(the)g(o)s(ccurrence)g(of)h(circuits)e (of)h Fu(\006)g FA(go)s(o)s(d)g(b)s(o)m(xes)118 2150 y(at)j(the)f(in)m(termediate)g(scale)g Fv(H)7 b FA(.)70 b(As)40 b(a)h(consequence,)i(the)e(surface)f(tension)f(factor)i(should) d(no)m(w)118 2258 y(b)s(e)k(related)g(to)h(the)g(asymptotic)g(of)f(the) h(ratio)f(of)h(partition)e(functions)g(with)g(statistically)g(pure)118 2366 y(b)s(oundary)28 b(conditions)h(at)i(the)g(scale)g Fv(H)7 b FA(.)218 2474 y(Let)36 b(us)g(giv)m(e)g(no)m(w)g(a)h(precise)e (mathematical)h(form)m(ulation)f(of)h(the)h(problem.)56 b(F)-8 b(or)36 b Fv(N)45 b Fu(2)34 b Fy(N)49 b FA(and)118 2582 y Fv(\016)29 b(>)c FA(0,)i(w)m(e)f(de\014ne)f(\003)830 2549 y Fs(\016)830 2609 y(N)923 2582 y FA(=)f Fu(f)p Fv(i)j Fu(2)d Fy(Z)1271 2549 y Fs(d)1398 2582 y Fu(j)i(j)p Fv(i)1505 2596 y Fx(1)1545 2582 y Fu(j)g Fr(6)e Fv(\016)s(N)5 b(;)42 b(k)28 b FA(=)d(2)p Fv(;)15 b(:)g(:)g(:)j(;)d(d;)41 b Fu(j)p Fv(i)2467 2597 y Fs(k)2510 2582 y Fu(j)26 b Fr(6)f Fv(N)10 b Fu(g)p FA(.)39 b(Let)26 b Fv(G)3078 2549 y Ft(\006)p Fs(;")3190 2582 y FA(\(\003)3288 2549 y Fs(\016)3288 2609 y(N)3356 2582 y FA(\))f(b)s(e)g(the)118 2691 y(set)37 b(of)f(mixed)g(b)s(oundary)e(conditions)h(\()p Fv(\033)1598 2658 y Fx(+)1657 2691 y Fv(;)15 b(\033)1752 2658 y Ft(\000)1812 2691 y FA(\))36 b(suc)m(h)g(that)h(the)g (con\014guration)e Fv(\033)3071 2658 y Fx(+)3167 2691 y FA(is)g(supp)s(orted)118 2798 y(b)m(y)e(the)f(domain)g Fu(f)p Fv(i)807 2812 y Fx(1)876 2798 y Fv(>)c(\016)s(N)10 b Fu(g)34 b FA(and)e(con)m(tains)h(mesoscopic)f(phase)h(lab)s(els)d Fv(\021)2746 2766 y Fs(")2743 2825 y(N)s(;H)2922 2798 y FA(uniformly)g(equal)i(to)118 2920 y(1.)46 b(Similarly)-8 b(,)29 b Fv(\033)695 2887 y Ft(\000)786 2920 y FA(is)i(supp)s(orted)f (b)m(y)h(the)h(domain)f Fu(f)p Fv(i)1994 2934 y Fx(1)2062 2920 y Fv(<)d Fu(\000)p Fv(\016)s(N)10 b Fu(g)32 b FA(and)g(con)m (tains)g(mesoscopic)g(phase)118 3028 y(lab)s(els)i Fv(\021)427 2995 y Fs(")424 3055 y(N)s(;H)605 3028 y FA(uniformly)f(equal)h(to)j Fu(\000)p FA(1.)55 b(The)35 b(partition)f(function)g(with)g(b)s (oundary)g(conditions)g(in)118 3175 y Fv(G)189 3142 y Ft(\006)p Fs(;")301 3175 y FA(\(\003)399 3142 y Fs(\016)399 3202 y(N)467 3175 y FA(\))h(is)g(denoted)g(b)m(y)h Fv(Z)1183 3131 y Fs(\033)1225 3108 y Fm(+)1276 3131 y Fs(;\033)1338 3108 y Fl(\000)1176 3216 y Fs(\015)t(;)p Fx(\003)1285 3193 y Fp(\016)1285 3239 y(N)1394 3175 y FA(.)56 b(Let)41 b(~)-50 b Fv(\033)1698 3142 y Ft(\000)1793 3175 y FA(b)s(e)35 b(the)h(con\014guration)f(deduced)f(from)h Fv(\033)3273 3142 y Ft(\000)3368 3175 y FA(b)m(y)g(spin)118 3311 y(\015ip.)50 b(In)33 b(the)h(deriv)-5 b(ation)33 b(of)h(the)h(lo)m(w)m(er)f(and)f (the)h(upp)s(er)e(b)s(ounds,)h(the)i(surface)f(tension)f(should)f(b)s (e)118 3419 y(related)e(to)i(the)e(follo)m(wing)f(appro)m(ximate)h (quan)m(tities)1503 3786 y(log)1636 3603 y Fq(0)1636 3767 y(@)1725 3687 y Fv(Z)1794 3643 y Fs(\033)1836 3619 y Fm(+)1887 3643 y Fs(;\033)1949 3619 y Fl(\000)1787 3727 y Fs(\015)t(;)p Fx(\003)1896 3705 y Fp(\016)1896 3751 y(N)p 1725 3765 281 4 v 1725 3871 a Fv(Z)1794 3827 y Fs(\033)1836 3808 y Fm(+)1887 3827 y Fs(;)t Fx(~)-39 b Fs(\033)1949 3808 y Fl(\000)1787 3912 y Fs(\015)t(;)p Fx(\003)1896 3889 y Fp(\016)1896 3935 y(N)2016 3603 y Fq(1)2016 3767 y(A)3475 3786 y FA(\(4.4\))118 4149 y(Ultimately)25 b(the)h(parameter)g Fv(\016)j FA(will)23 b(v)-5 b(anish)24 b(and)h(therefore)i(the)e(b)s(oundary)f(conditions)g(on)i(the)g(faces) 118 4257 y(of)31 b(\003)285 4224 y Fs(\016)285 4284 y(N)384 4257 y FA(parallel)e(to)g Fv(~)-42 b(e)862 4271 y Fx(1)933 4257 y FA(can)32 b(b)s(e)e(c)m(hosen)i(arbitrarily)-8 b(.)41 b(F)-8 b(or)32 b(con)m(v)m(enience)g(w)m(e)g(\014x)e(these)i (conditions)e(to)118 4365 y(b)s(e)g(equal)g(to)h Fv(m)673 4332 y Ft(\003)673 4392 y Fs(\014)720 4365 y FA(.)218 4482 y(The)g(surface)g(tension)g(is)f(de\014ned)g(for)h(arbitrary)f (directions)g(and)h(general)h(domains)e(\(see)i(\(2.2\))r(\).)118 4592 y(T)-8 b(o)31 b(simplify)d(the)j(notation,)g(w)m(e)h(will)c (consider)i(only)g(the)h(direction)c Fv(~)-43 b(n)26 b FA(=)c Fv(~)-41 b(e)2761 4606 y Fx(1)2831 4592 y FA(and)30 b(domains)g(\001)3444 4559 y Fs(\016)3444 4619 y(N)3511 4592 y FA(.)42 b(In)118 4700 y(fact,)32 b(the)e(results)f(also)i(hold)e (for)h(arbitrary)f(directions)d Fv(~)-42 b(n)30 b FA(and)g(domains.)118 4922 y FF(Remark)37 b(4.1.)43 b Fn(Notic)-5 b(e)35 b(that)h(the)f (mesosc)-5 b(opic)36 b(phase)g(lab)-5 b(els)35 b(on)h(the)f(sc)-5 b(ale)35 b Fv(K)41 b Fn(ar)-5 b(e)36 b(now)f(built)f(with)118 5030 y(blo)-5 b(cks)35 b(of)g(spins)g(at)g(the)g(sc)-5 b(ale)35 b Fv(H)h FA(=)29 b(2)1464 4997 y Fs(h)1509 5030 y Fv(\015)1561 4997 y Ft(\000)p Fx(1)1655 5030 y Fn(.)48 b(Ther)-5 b(efor)g(e)36 b(the)f(mesosc)-5 b(opic)36 b(sur)-5 b(gery)35 b(involves)g(blo)-5 b(cks)118 5138 y(of)35 b(spins)h(and)g(the)g(err)-5 b(or)36 b(term)g(is)f(of)g(or)-5 b(der)37 b FA(exp\()1885 5102 y Fx(1)p 1883 5117 41 4 v 1883 5169 a Fs(\015)1934 5138 y FA(\))p Fn(.)49 b(This)36 b(is)f(actual)5 b(ly)36 b(not)f(a)h(pr)-5 b(oblem)37 b(b)-5 b(e)g(c)g(ause)35 b Fv(\015)118 5258 y Fn(is)e(\014xe)-5 b(d)33 b(and)h(these)f(terms)g(disapp)-5 b(e)g(ar)36 b(in)c(the)h(limit)g(\()p Fv(\016)d Fu(!)25 b FA(0)p Fn(\).)118 5480 y FA(4.3.)47 b FF(Lo)m(w)m(er)35 b(b)s(ound.)p eop %%Page: 23 23 23 22 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(23)118 366 y FF(Prop)s(osition)37 b(4.1.)43 b Fn(L)-5 b(et)33 b Fv(\014)f(>)26 b FA(1)33 b Fn(and)i(\014x)e Fv(\015)1655 381 y Fs(\014)1729 366 y Fv(>)26 b FA(0)p Fn(,)33 b Fv(")27 b(>)f FA(0)34 b Fn(such)f(that)i(The)-5 b(or)g(ems)35 b(4.1)f(and)g(4.2)g(hold.)118 474 y(F)-7 b(or)34 b(al)5 b(l)33 b Fv(\015)d(<)25 b(\015)638 489 y Fs(\014)685 474 y Fn(,)853 749 y FA(lim)847 811 y Fs(\016)r Ft(!)p Fx(0)1001 749 y FA(lim)15 b(inf)1025 810 y Fs(N)7 b Ft(!1)1362 688 y FA(1)p 1278 728 214 4 v 1278 812 a Fv(N)1361 785 y Fs(d)p Ft(\000)p Fx(1)1566 749 y FA(inf)1517 815 y Fs(\033)1559 796 y Fm(+)1611 815 y Fs(;\033)1673 796 y Fl(\000)1740 749 y FA(log)1873 567 y Fq(0)1873 730 y(@)1962 650 y Fv(Z)2031 606 y Fs(\033)2073 582 y Fm(+)2124 606 y Fs(;\033)2186 582 y Fl(\000)2024 691 y Fs(\015)t(;)p Fx(\003)2133 668 y Fp(\016)2133 714 y(N)p 1962 728 281 4 v 1962 834 a Fv(Z)2031 790 y Fs(\033)2073 771 y Fm(+)2124 790 y Fs(;)t Fx(~)-39 b Fs(\033)2186 771 y Fl(\000)2024 875 y Fs(\015)t(;)p Fx(\003)2133 852 y Fp(\016)2133 898 y(N)2253 567 y Fq(1)2253 730 y(A)2373 749 y Fr(>)45 b Fu(\000)20 b Fv(\034)2620 764 y Fs(\014)s(;\015)2742 749 y Fv(;)708 b FA(\(4.5\))118 1020 y Fn(wher)-5 b(e)33 b(the)g(in\014mum)f(is)g(taken)h(over)f(the)h(b)-5 b(oundary)34 b(c)-5 b(on\014gur)g(ations)34 b(such)e(that)i FA(\()p Fv(\033)3030 987 y Fx(+)3089 1020 y Fv(;)15 b(\033)3184 987 y Ft(\000)3244 1020 y FA(\))32 b Fn(b)-5 b(elong)33 b(to)118 1130 y Fv(G)189 1097 y Ft(\006)p Fs(;")301 1130 y FA(\(\003)399 1097 y Fs(\016)399 1157 y(N)467 1130 y FA(\))p Fn(.)118 1293 y(Pr)-5 b(o)g(of.)43 b FA(If)38 b(the)h(b)s(oundary)e(conditions)g(are)i Fv(\033)1739 1260 y Fx(+)1837 1293 y FA(=)g(1)g(and)f Fv(\033)2271 1260 y Ft(\000)2369 1293 y FA(=)h Fu(\000)p FA(1)g(then,)h(b)m(y)f (de\014nition)d(of)j(the)118 1401 y(surface)27 b(tension,)h(\(4.5\))h (holds.)38 b(W)-8 b(e)28 b(are)g(going)f(to)h(in)m(terp)s(olate)f(b)s (et)m(w)m(een)g(the)h(b)s(oundary)d(conditions)118 1509 y(\()p Fv(\033)208 1476 y Fx(+)268 1509 y Fv(;)15 b(\033)363 1476 y Ft(\000)422 1509 y FA(\))36 b(and)f(\(1)p Fv(;)15 b Fu(\000)p FA(1\).)57 b(F)-8 b(or)36 b(simplicit)m(y)-8 b(,)35 b(the)g(dep)s(endency)f(on)h Fv(\015)41 b FA(and)34 b Fv(\016)39 b FA(will)33 b(b)s(e)i(omitted)g(in)f(the)118 1640 y(notation)d(and)f(the)g(partition)f(function)g(will)f(b)s(e)i (denoted)g(b)m(y)g Fv(Z)2384 1595 y Fs(\033)2426 1572 y Fm(+)2477 1595 y Fs(;\033)2539 1572 y Fl(\000)2377 1668 y Fs(N)2596 1640 y FA(.)218 1856 y(First)f(w)m(e)i(are)g(going)f (to)i(c)m(hec)m(k)g(that)804 2085 y(lim)15 b(inf)828 2146 y Fs(N)7 b Ft(!1)1165 2024 y FA(1)p 1081 2064 214 4 v 1081 2147 a Fv(N)1164 2121 y Fs(d)p Ft(\000)p Fx(1)1368 2085 y FA(inf)1320 2151 y Fs(\033)1362 2132 y Fm(+)1413 2151 y Fs(;\033)1475 2132 y Fl(\000)1543 1930 y Fq(")1596 2085 y FA(log)1738 2021 y Fv(Z)1807 1977 y Fs(\033)1849 1953 y Fm(+)1900 1977 y Fs(;\033)1962 1953 y Fl(\000)1800 2050 y Fs(N)p 1738 2064 281 4 v 1738 2170 a Fv(Z)1807 2126 y Fs(\033)1849 2107 y Fm(+)1900 2126 y Fs(;)t Fx(~)-39 b Fs(\033)1962 2107 y Fl(\000)1800 2199 y Fs(N)2049 2085 y Fu(\000)20 b FA(log)2282 2021 y Fv(Z)2351 1977 y Fx(+)p Fs(;\033)2468 1953 y Fl(\000)2344 2050 y Fs(N)p 2282 2064 243 4 v 2282 2170 a Fv(Z)2351 2126 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)2468 2107 y Fl(\000)2344 2199 y Fs(N)2534 1930 y Fq(#)2628 2085 y Fr(>)25 b FA(0)15 b Fv(:)666 b FA(\(4.6\))218 2337 y(F)-8 b(or)23 b(a)g(giv)m(en)f(b)s(oundary)e (condition)h Fv(\033)1517 2304 y Fx(+)1576 2337 y FA(,)j(w)m(e)f (de\014ne)f(\003)2069 2293 y Fs(\016)o(;)p Fx(+)2069 2366 y Fs(N)2200 2337 y FA(as)g(the)h(subset)e(of)i Fu(f)p Fv(i)2894 2351 y Fx(1)2959 2337 y Fv(>)i(\016)s(N)10 b Fu(g)24 b FA(con)m(taining)118 2465 y(the)31 b(sites)f Fv(i)g FA(suc)m(h)g(that)h Fv(\033)996 2426 y Fx(+)993 2492 y Fs(i)1081 2465 y FA(=)25 b Fu(\000)p FA(1.)41 b(F)-8 b(or)31 b(an)m(y)f Fv(i)c Fu(2)f FA(\003)1899 2420 y Fs(\016)o(;)p Fx(+)1899 2493 y Fs(N)2007 2465 y FA(,)31 b(w)m(e)g(set)1016 2620 y Fu(8)p Fv(s)24 b Fu(2)h FA([0)p Fv(;)15 b FA(1])p Fv(;)199 b(\033)1679 2582 y Fx(+)1676 2647 y Fs(i)1738 2620 y FA(\()p Fv(s)p FA(\))26 b(=)f(\(1)c Fu(\000)f Fv(\033)2220 2582 y Fx(+)2217 2647 y Fs(i)2279 2620 y FA(\))p Fv(s)g FA(+)g Fv(\033)2523 2582 y Fx(+)2520 2647 y Fs(i)118 2768 y FA(and)30 b(b)m(y)g(in)m (tegrating)127 2998 y(log)269 2934 y Fv(Z)338 2889 y Fx(+)p Fs(;\033)455 2866 y Fl(\000)331 2962 y Fs(N)p 269 2977 V 269 3083 a Fv(Z)338 3038 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)455 3019 y Fl(\000)331 3111 y Fs(N)541 2998 y Fu(\000)20 b FA(log)775 2934 y Fv(Z)844 2889 y Fs(\033)886 2866 y Fm(+)937 2889 y Fs(;\033)999 2866 y Fl(\000)837 2962 y Fs(N)p 775 2977 281 4 v 775 3083 a Fv(Z)844 3038 y Fs(\033)886 3019 y Fm(+)937 3038 y Fs(;)t Fx(~)-39 b Fs(\033)999 3019 y Fl(\000)837 3111 y Fs(N)1091 2998 y FA(=)1332 2911 y Fq(X)1187 3130 y Fs(i)p Ft(2)p Fx(\003)1307 3097 y Fp(\016)n(;)p Fm(+)1307 3153 y Fp(N)1403 3130 y Fs(;j)t Ft(2)p Fx(\003)1552 3107 y Fp(\016)1552 3153 y(N)1624 2874 y Fq(Z)1715 2900 y Fx(1)1674 3080 y(0)1784 2998 y Fv(ds)15 b(J)1939 3012 y Fs(\015)1984 2998 y FA(\()p Fv(i;)g(j)5 b FA(\))2182 2897 y Fq(\020)2239 2998 y Fv(\026)2294 2950 y Fs(\033)2336 2926 y Fm(+)2387 2950 y Fx(\()p Fs(s)p Fx(\))p Fs(;\033)2536 2926 y Fl(\000)2294 3027 y Fs(\014)s(;\015)t(;N) 2593 2998 y FA(\()p Fv(\033)2680 3012 y Fs(j)2717 2998 y FA(\))21 b Fu(\000)e Fv(\026)2918 2950 y Fs(\033)2960 2926 y Fm(+)3012 2950 y Fx(\()p Fs(s)p Fx(\))p Fs(;)t Fx(~)-39 b Fs(\033)3161 2926 y Fl(\000)2918 3027 y Fs(\014)s(;\015)t (;N)3218 2998 y FA(\()p Fv(\033)3305 3012 y Fs(j)3342 2998 y FA(\))3377 2897 y Fq(\021)3462 2998 y Fv(:)218 3274 y FA(The)30 b(RHS)g(can)g(b)s(e)g(split)e(in)m(to)j(t)m(w)m(o)h (terms.)40 b(The)30 b(\014rst)g(one)g(is)g(non)f(p)s(ositiv)m(e)h(b)m (y)g(FK)m(G)h(inequalit)m(y)739 3393 y Fq(X)593 3612 y Fs(i)p Ft(2)p Fx(\003)713 3580 y Fp(\016)n(;)p Fm(+)713 3635 y Fp(N)810 3612 y Fs(;j)t Ft(2)p Fx(\003)959 3589 y Fp(\016)959 3635 y(N)1030 3356 y Fq(Z)1121 3382 y Fx(1)1081 3562 y(0)1191 3480 y Fv(ds)15 b(J)1346 3494 y Fs(\015)1391 3480 y FA(\()p Fv(i;)g(j)5 b FA(\))1589 3379 y Fq(\020)1646 3480 y Fv(\026)1701 3432 y Fs(\033)1743 3408 y Fm(+)1794 3432 y Fx(\()p Fs(s)p Fx(\))p Fs(;\033)1943 3408 y Fl(\000)1701 3509 y Fs(\014)s(;\015)t(;N)2000 3480 y FA(\()p Fv(\033)2087 3494 y Fs(j)2124 3480 y FA(\))20 b Fu(\000)g Fv(\026)2325 3432 y Fs(\033)2367 3408 y Fm(+)2418 3432 y Fx(\()p Fs(s)p Fx(\))p Fs(;)p Fx(+)2325 3509 y Fs(\014)s(;\015)t(;N)2585 3480 y FA(\()p Fv(\033)2672 3494 y Fs(j)2708 3480 y FA(\))2743 3379 y Fq(\021)2838 3480 y Fr(6)25 b FA(0)15 b Fv(:)118 3756 y FA(The)30 b(second)g(term)850 3858 y Fq(X)704 4077 y Fs(i)p Ft(2)p Fx(\003)824 4044 y Fp(\016)n(;)p Fm(+)824 4100 y Fp(N)921 4077 y Fs(;j)t Ft(2)p Fx(\003)1070 4054 y Fp(\016)1070 4100 y(N)1142 3821 y Fq(Z)1232 3847 y Fx(1)1192 4027 y(0)1302 3944 y Fv(ds)15 b(J)1457 3958 y Fs(\015)1502 3944 y FA(\()p Fv(i;)g(j)5 b FA(\))1700 3844 y Fq(\020)1757 3944 y Fv(\026)1812 3897 y Fs(\033)1854 3873 y Fm(+)1905 3897 y Fx(\()p Fs(s)p Fx(\))p Fs(;)p Fx(+)1812 3974 y Fs(\014)s(;\015)t(;N)2071 3944 y FA(\()p Fv(\033)2158 3958 y Fs(j)2195 3944 y FA(\))20 b Fu(\000)g Fv(\026)2396 3897 y Fs(\033)2438 3873 y Fm(+)2490 3897 y Fx(\()p Fs(s)p Fx(\))p Fs(;)t Fx(~)-39 b Fs(\033)2639 3873 y Fl(\000)2396 3974 y Fs(\014)s(;\015)t(;N)2696 3944 y FA(\()p Fv(\033)2783 3958 y Fs(j)2819 3944 y FA(\))2854 3844 y Fq(\021)3475 3944 y FA(\(4.7\))118 4220 y(will)41 b(b)s(e)h(ev)-5 b(aluated)43 b(b)m(y)g(using)f(the)h(exp)s(onen)m(tial) f(deca)m(y)i(of)f(correlations.)79 b(W)-8 b(e)44 b(need)f(to)h(state)g (a)118 4328 y(result)33 b(sligh)m(tly)f(stronger)i(than)f(Theorem)h (4.2,)i(whose)e(pro)s(of)f(is)g(implicitly)d(con)m(tained)k(in)e([BMP)q (].)118 4436 y(F)-8 b(or)43 b(a)f(giv)m(en)f(domain)g(\001,)j(the)e (extended)g(set)g(of)g(b)s(oundary)d(conditions)i Fu(G)2868 4403 y Fx(+)p Fs(;")2979 4436 y FA(\(\001\))h(con)m(tains)g(the)118 4544 y(con\014gurations)30 b Fv(\033)757 4558 y Fx(\001)816 4539 y Fp(c)882 4544 y FA(suc)m(h)g(that)1055 4711 y Fu(8)p Fy(B)1160 4725 y Fs(L)1218 4711 y FA(\()p Fv(y)s FA(\))c Fu(\032)f FA(\001)1534 4673 y Fs(c)1568 4711 y Fv(;)197 b Fu(M)1899 4725 y Fs(N)s(;L)2030 4711 y FA(\()p Fv(y)s FA(\))21 b Fu(\000)f Fv(m)2340 4673 y Ft(\003)2340 4734 y Fs(\014)2412 4711 y Fr(>)45 b Fu(\000)2631 4649 y Fv(")p 2629 4690 46 4 v 2629 4773 a FA(2)2700 4711 y Fv(:)118 4885 y FA(In)30 b(particular,)f(the)h(b)s(oundary)f (conditions)f(uniformly)g(equal)i(to)h(1)g(b)s(elong)e(to)i(this)e (set.)118 5048 y FF(Theorem)43 b(4.4.)j Fn(F)-7 b(or)40 b(any)g Fv(\014)j(>)37 b FA(1)p Fn(,)42 b(ther)-5 b(e)40 b(exists)g Fv(\015)1989 5063 y Fs(\014)2074 5048 y Fv(>)d FA(0)j Fn(and)g Fv(")2492 5015 y Ft(\003)2492 5076 y Fs(\014)2579 5048 y Fn(such)f(that)i(for)f Fv(")e Fu(2)p FA(]0)p Fv(;)15 b(")3430 5015 y Ft(\003)3430 5076 y Fs(\014)3478 5048 y FA([)40 b Fn(the)118 5176 y(fol)5 b(lowing)32 b(holds.)42 b(F)-7 b(or)32 b(any)f(subset)f FA(\001)g Fn(of)h Fy(Z)1653 5143 y Fs(d)1689 5176 y Fn(,)g(let)g FA(\()p Fv(\033)n(;)15 b(\033)2054 5143 y Ft(0)2078 5176 y FA(\))31 b Fn(b)-5 b(e)30 b(two)h(c)-5 b(on\014gur)g(ations)33 b(in)e Fu(G)3169 5143 y Fx(+)p Fs(;")3280 5176 y FA(\(\001)3391 5143 y Fs(c)3426 5176 y FA(\))g Fn(then)118 5284 y(for)i Fv(K)f Fu(\032)25 b FA(\001)p Fn(,)32 b(one)h(has)382 5454 y Fu(8)p Fv(\015)d Fr(6)25 b Fv(\015)653 5469 y Fs(\014)700 5454 y Fv(;)927 5350 y Fq(\014)927 5404 y(\014)927 5459 y(\014)957 5454 y Fv(\026)1012 5417 y Fs(\033)1012 5478 y(\014)s(;\015)t(;)p Fx(\001)1197 5454 y FA(\()p Fv(\033)1284 5468 y Ft(K)1343 5454 y FA(\))20 b Fu(\000)g Fv(\026)1544 5417 y Fs(\033)1586 5393 y Fl(0)1544 5478 y Fs(\014)s(;\015)t(;)p Fx(\001)1729 5454 y FA(\()p Fv(\033)1816 5468 y Ft(K)1875 5454 y FA(\))1910 5350 y Fq(\014)1910 5404 y(\014)1910 5459 y(\014)1966 5454 y Fr(6)25 b Fu(jK)q(j)15 b FA(exp)2352 5381 y Fq(\000)2414 5454 y Fu(\000)20 b Fv(c)p FA(\()p Fv(")p FA(\))p Fv(\015)2708 5417 y Fx(2)2764 5454 y Fn(dist)q FA(\()p Fu(K)q Fv(;)15 b Fu(S)7 b FA(\))3148 5381 y Fq(\001)3206 5454 y Fv(;)p eop %%Page: 24 24 24 23 bop 118 45 a Fx(24)1460 b(T.)23 b(BODINEA)n(U)118 366 y Fn(wher)-5 b(e)34 b Fu(S)39 b Fn(is)33 b(the)g(subset)f(of)h FA(\001)1170 333 y Fs(c)1237 366 y Fn(wher)-5 b(e)34 b Fv(\033)i Fn(and)d Fv(\033)1813 333 y Ft(0)1869 366 y Fn(di\013er)g(and)h Fv(c)p FA(\()p Fv(")p FA(\))g Fn(is)e(a)h(p)-5 b(ositive)34 b(c)-5 b(onstant.)218 529 y FA(The)39 b(b)s(oundary)e (conditions)h(\()p Fv(\033)1366 496 y Fx(+)1425 529 y FA(\()p Fv(s)p FA(\))p Fv(;)21 b FA(~)-51 b Fv(\033)1633 496 y Ft(\000)1693 529 y FA(\))40 b(and)f(\()p Fv(\033)2044 496 y Fx(+)2103 529 y FA(\()p Fv(s)p FA(\))p Fv(;)15 b FA(+\))40 b(di\013er)e(only)h(in)f(the)h(lo)m(w)m(er)h(part)f(of)118 639 y(\(\003)216 606 y Fs(\016)216 666 y(N)284 639 y FA(\))319 606 y Fs(c)354 639 y FA(,)30 b(th)m(us)g(the)h(exp)s(onen)m (tial)e(relaxation)h(enables)g(us)g(to)h(ev)-5 b(aluate)31 b(\(4.7\))848 876 y(log)991 812 y Fv(Z)1060 768 y Fx(+)p Fs(;\033)1177 744 y Fl(\000)1053 841 y Fs(N)p 991 855 243 4 v 991 961 a Fv(Z)1060 917 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)1177 898 y Fl(\000)1053 990 y Fs(N)1268 876 y Fr(6)40 b FA(log)1522 812 y Fv(Z)1591 768 y Fs(\033)1633 744 y Fm(+)1684 768 y Fs(;\033)1746 744 y Fl(\000)1584 841 y Fs(N)p 1522 855 281 4 v 1522 961 a Fv(Z)1591 917 y Fs(\033)1633 898 y Fm(+)1684 917 y Fs(;)t Fx(~)-39 b Fs(\033)1746 898 y Fl(\000)1584 990 y Fs(N)1832 876 y FA(+)1933 815 y Fv(N)2016 782 y Fs(d)p Ft(\000)p Fx(1)p 1933 855 214 4 v 1994 938 a Fv(\015)2046 912 y Fs(d)2172 876 y FA(exp\()p Fu(\000)p Fv(c\015)2508 839 y Fx(2)2563 876 y Fv(\016)s(N)10 b FA(\))15 b Fv(:)118 1100 y FA(This)28 b(estimate)i(holds)e(uniformly)f(o)m(v)m(er)j(the)g(b)s(oundary)d (conditions.)39 b(Letting)30 b Fv(N)39 b FA(go)31 b(to)f(in\014nit)m(y) -8 b(,)28 b(w)m(e)118 1207 y(deriv)m(e)i(\(4.6\))i(.)218 1423 y(It)e(remains)f(to)i(c)m(hec)m(k)h(that)1290 1634 y Fu(8)p Fv(\033)1396 1596 y Ft(\000)1455 1634 y Fv(;)1687 1569 y(Z)1756 1525 y Fx(+)p Fs(;\033)1873 1502 y Fl(\000)1749 1598 y Fs(N)p 1687 1613 243 4 v 1687 1719 a Fv(Z)1756 1674 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)1873 1655 y Fl(\000)1749 1747 y Fs(N)1965 1634 y Fr(>)2071 1569 y Fv(Z)2140 1525 y Fx(+)p Fs(;)p Ft(\000)2133 1598 y Fs(N)p 2071 1613 203 4 v 2071 1708 a Fv(Z)2140 1664 y Fx(+)p Fs(;)p Fx(+)2133 1737 y Fs(N)2298 1634 y Fv(:)1152 b FA(\(4.8\))118 1857 y(This)29 b(follo)m(ws)g(from)h(FK)m(G)h(inequalit)m(y)-8 b(.)40 b(By)30 b(in)m(terp)s(olating,)f(w)m(e)i(get)204 2085 y(log)346 2021 y Fv(Z)415 1977 y Fx(+)p Fs(;\033)532 1953 y Fl(\000)408 2049 y Fs(N)p 346 2064 243 4 v 346 2170 a Fv(Z)415 2126 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)532 2107 y Fl(\000)408 2198 y Fs(N)619 2085 y Fu(\000)19 b FA(log)852 2021 y Fv(Z)921 1977 y Fx(+)p Fs(;)p Ft(\000)914 2049 y Fs(N)p 852 2064 203 4 v 852 2159 a Fv(Z)921 2115 y Fx(+)p Fs(;)p Fx(+)914 2188 y Fs(N)1089 2085 y FA(=)1331 1999 y Fq(X)1185 2217 y Fs(i)p Ft(2)p Fx(\003)1305 2185 y Fp(\016)n(;)p Fl(\000)1305 2240 y Fp(N)1403 2217 y Fs(;j)t Ft(2)p Fx(\003)1552 2194 y Fp(\016)1552 2240 y(N)1624 1961 y Fq(Z)1715 1987 y Fx(1)1674 2167 y(0)1784 2085 y Fv(ds)c(J)1939 2099 y Fs(\015)1984 2085 y FA(\()p Fv(i;)g(j)5 b FA(\))2182 1984 y Fq(\020)2239 2085 y Fv(\026)2294 2037 y Fx(+)p Fs(;\033)2411 2014 y Fl(\000)2463 2037 y Fx(\()p Fs(s)p Fx(\))2294 2114 y Fs(\014)s(;\015)t(;N)2555 2085 y FA(\()p Fv(\033)2642 2099 y Fs(j)2678 2085 y FA(\))21 b(+)f Fv(\026)2880 2037 y Fx(+)p Fs(;)t Fx(~)-39 b Fs(\033)2997 2014 y Fl(\000)3049 2037 y Fx(\()p Fs(s)p Fx(\))2880 2114 y Fs(\014)s(;\015)t(;N)3141 2085 y FA(\()p Fv(\033)3228 2099 y Fs(j)3264 2085 y FA(\))3299 1984 y Fq(\021)3384 2085 y Fv(;)118 2386 y FA(where)40 b(\003)454 2342 y Fs(\016)o(;)p Ft(\000)454 2415 y Fs(N)603 2386 y FA(is)g(de\014ned)f (in)g(a)i(similar)d(w)m(a)m(y)k(as)f(\003)1919 2342 y Fs(\016)o(;)p Fx(+)1919 2415 y Fs(N)2027 2386 y FA(.)71 b(The)40 b(spin)f(\015ip)g(symmetry)h(enables)g(us)g(to)118 2494 y(rewrite)29 b(the)h(RHS.)f(As)g(FK)m(G)i(inequalit)m(y)d(implies) e(that)31 b(the)e(magnetization)h(is)f(increasing)f(wrt)h(the)118 2602 y(b)s(oundary)f(\014elds)757 2721 y Fq(X)611 2939 y Fs(i)p Ft(2)p Fx(\003)731 2907 y Fp(\016)n(;)p Fl(\000)731 2962 y Fp(N)829 2939 y Fs(;j)t Ft(2)p Fx(\003)978 2916 y Fp(\016)978 2962 y(N)1050 2683 y Fq(Z)1141 2710 y Fx(1)1100 2889 y(0)1210 2807 y Fv(ds)15 b(J)1365 2821 y Fs(\015)1410 2807 y FA(\()p Fv(i;)g(j)5 b FA(\))1608 2706 y Fq(\020)1665 2807 y Fv(\026)1720 2759 y Fx(+)p Fs(;\033)1837 2736 y Fl(\000)1889 2759 y Fx(\()p Fs(s)p Fx(\))1720 2836 y Fs(\014)s(;\015)t(;N)1981 2807 y FA(\()p Fv(\033)2068 2821 y Fs(j)2104 2807 y FA(\))21 b Fu(\000)f Fv(\026)2306 2759 y Ft(\000)p Fs(;\033)2423 2736 y Fl(\000)2475 2759 y Fx(\()p Fs(s)p Fx(\))2306 2836 y Fs(\014)s(;\015)t(;N)2567 2807 y FA(\()p Fv(\033)2654 2821 y Fs(j)2690 2807 y FA(\))2725 2706 y Fq(\021)2820 2807 y Fr(>)25 b FA(0)15 b Fv(:)218 3081 y FA(Therefore)30 b(the)g(prop)s(osition)e(is)i(complete.)1857 b Fr(\003)118 3244 y FF(Remark)51 b(4.2.)f Fn(A)45 b(pr)-5 b(o)g(of)48 b(of)e(the)g(lower)h(b)-5 b(ound)47 b(without)g(using)e(FK) n(G)h(ine)-5 b(quality)46 b(c)-5 b(an)47 b(b)-5 b(e)46 b(done)118 3351 y(along)d(the)g(lines)g(of)f(the)h(pr)-5 b(o)g(of)45 b(of)d(the)h(upp)-5 b(er)43 b(b)-5 b(ound.)72 b(Nevertheless,)45 b(this)e(would)h(involve)e(mor)-5 b(e)118 3459 y(te)g(chnic)g(alities)39 b(b)-5 b(e)g(c)g(ause)38 b(another)h(ar)-5 b(gument)39 b(would)f(b)-5 b(e)38 b(r)-5 b(e)g(quir)g(e)g(d)38 b(to)g(r)-5 b(eplac)g(e)46 b FA(\(4.10\))s Fn(.)56 b(This)37 b(c)-5 b(an)38 b(b)-5 b(e)118 3567 y(achieve)g(d)34 b(by)e(c)-5 b(onsidering)34 b(r)-5 b(ough)34 b(minimal)f(se)-5 b(ctions)34 b FA(\()p Fu(S)2125 3534 y Fx(+)2184 3567 y Fv(;)15 b Fu(S)2286 3534 y Ft(\000)2345 3567 y FA(\))33 b Fn(inste)-5 b(ad)34 b(of)f(rigid)g(ones.)118 3732 y FA(4.4.)47 b FF(Upp)s(er)37 b(b)s(ound.)46 b FA(F)-8 b(or)32 b(some)g(b)s(oundary)d(conditions)h(in)h Fv(G)2412 3699 y Ft(\006)p Fs(;")2523 3732 y FA(\(\003)2621 3699 y Fs(\016)2621 3759 y(N)2689 3732 y FA(\),)h(the)g(quan)m(tit)m(y)h (\(4.4\))g(is)e(a)118 3840 y(bad)37 b(appro)m(ximation)f(of)h(the)h (surface)f(tension.)60 b(Some)37 b(b)s(oundary)f(conditions)f(in)m (teract)j(with)e(the)118 3948 y(in)m(terface)31 b(and)f(one)g(should)f (exp)s(ect)i(the)f(follo)m(wing)f(lo)m(w)m(er)i(b)s(ound)658 4211 y(lim)652 4272 y Fs(\016)r Ft(!)p Fx(0)807 4211 y FA(lim)15 b(sup)844 4289 y Fs(N)7 b Ft(!1)1194 4149 y FA(1)p 1110 4190 214 4 v 1110 4273 a Fv(N)1193 4247 y Fs(d)p Ft(\000)p Fx(1)1594 4211 y FA(sup)1349 4301 y Fx(\()p Fs(\033)1418 4282 y Fm(+)1470 4301 y Fs(;\033)1532 4282 y Fl(\000)1584 4301 y Fx(\))p Ft(2)p Fs(G)1713 4282 y Fl(\006)p Fp(;")1814 4301 y Fx(\(\003)1890 4278 y Fp(\016)1890 4324 y(N)1948 4301 y Fx(\))1990 4211 y FA(log)2123 4028 y Fq(0)2123 4192 y(@)2212 4112 y Fv(Z)2281 4067 y Fs(\033)2323 4044 y Fm(+)2374 4067 y Fs(;\033)2436 4044 y Fl(\000)2274 4152 y Fs(\015)t(;)p Fx(\003)2383 4129 y Fp(\016)2383 4175 y(N)p 2212 4190 281 4 v 2212 4296 a Fv(Z)2281 4252 y Fs(\033)2323 4233 y Fm(+)2374 4252 y Fs(;)t Fx(~)-39 b Fs(\033)2436 4233 y Fl(\000)2274 4336 y Fs(\015)t(;)p Fx(\003)2383 4314 y Fp(\016)2383 4360 y(N)2503 4028 y Fq(1)2503 4192 y(A)2608 4211 y Fv(>)25 b Fu(\000)p Fv(\034)2815 4226 y Fs(\014)s(;\015)2936 4211 y Fv(:)118 4469 y FA(In)38 b(order)h(to)h(screen)f(the)g(in\015uence)e(of)i(the)h(b)s(oundary)d (conditions,)i(one)h(is)e(lead)g(to)i(in)m(tro)s(duce)e(a)118 4577 y(di\013eren)m(t)h(appro)m(ximation)f(of)h(the)h(surface)f (tension.)66 b(This)38 b(is)g(done)h(b)m(y)g(lo)s(calizing)e(the)j(in)m (terface)118 4685 y(a)m(w)m(a)m(y)33 b(from)e(the)g(b)s(oundary)e(with) h(the)i(help)d(of)j(t)m(w)m(o)g(extra)g(minimal)d(sections)i(whic)m(h)f (decouple)g(the)118 4793 y(in)m(terface)h(and)f(the)g(b)s(oundary)f (conditions.)218 5009 y(Mimic)m(king)22 b(the)i(argumen)m(t)g(used)f (for)h(the)g(deriv)-5 b(ation)22 b(of)i(the)g(upp)s(er)e(b)s(ound)g (\(subsection)h(3.4\),)k(w)m(e)118 5117 y(can)k(\014nd)e(4)i(minimal)d (sections)i(in)f(eac)m(h)j(cub)s(e)e Fv(R)1832 5084 y Fs(i)1831 5144 y(N)1929 5117 y FA(of)g(heigh)m(t)h Fv(\016)s(hN)10 b FA(.)42 b(Let)31 b(us)f(denote)h(b)m(y)f Fv(Q)3324 5084 y Fs(i)3324 5144 y(N)3391 5117 y FA(\()p Fv(s)p FA(\))h(the)118 5229 y(parallelepip)s(ed)g(included)g(in)i Fv(R)1253 5196 y Fs(i)1252 5256 y(N)1353 5229 y FA(with)g(basis)g Fv(B)1865 5196 y Fs(i)1927 5229 y FA(and)h(heigh)m(t)g Fv(sN)10 b FA(.)51 b(There)34 b(is)f(a)i(minimal)c(section)118 5353 y(in)37 b Fv(R)302 5308 y Fs(i;)p Fx(+)301 5381 y Fs(N)430 5353 y Fu(\\)25 b Fv(Q)588 5320 y Fs(i)588 5379 y(N)655 5353 y FA(\()700 5317 y Fs(\016)r(h)p 700 5332 75 4 v 720 5384 a Fx(4)784 5353 y Fv(N)10 b FA(\))39 b(and)e(another)h(in)f Fv(R)1650 5308 y Fs(i;)p Fx(+)1649 5381 y Fs(N)1778 5353 y Fu(n)26 b Fv(Q)1921 5320 y Fs(i)1921 5379 y(N)1988 5353 y FA(\()2033 5317 y Fx(3)p Fs(\016)r(h)p 2033 5332 110 4 v 2070 5384 a Fx(2)2153 5353 y Fv(N)10 b FA(\).)64 b(By)38 b(symmetry)-8 b(,)41 b(there)d(exist)g(also)g(2)118 5480 y(minimal)28 b(sections)i(in)f Fv(R)987 5436 y Fs(i;)p Ft(\000)986 5509 y Fs(N)1089 5480 y FA(.)p eop %%Page: 25 25 25 24 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(25)218 366 y FA(By)40 b(applying)d(the)j (surgical)e(pro)s(cedure,)j(w)m(e)f(deduce)f(from)g(the)h Fy(L)2618 333 y Fx(1)2702 366 y FA(constrain)m(t)g(the)g(existence)118 474 y(of)34 b(2)h(surfaces)f(of)g(+)g(go)s(o)s(d)g(blo)s(c)m(ks)g (\(resp)f Fu(\000)p FA(\))i(at)f(the)h(mesoscopic)f(scale)h Fv(H)41 b FA(crossing)33 b(the)i(domains)118 594 y Fv(R)188 549 y Fs(i;)p Fx(+)187 622 y Fs(N)326 594 y FA(\(resp)g Fv(R)629 549 y Fs(i;)p Ft(\000)628 622 y Fs(N)731 594 y FA(\).)56 b(After)36 b(conditioning)d(wrt)i(the)g Fu(\006)g FA(surfaces)g(whic)m(h)f(are)i(the)g(closest)f(to)h(\()p Fv(R)3499 561 y Fs(i)3498 621 y(N)3566 594 y FA(\))3601 561 y Fs(c)3636 594 y FA(,)118 702 y(it)30 b(remains)g(to)i(consider)d (a)i(partition)f(function)f(with)h(mixed)f(b)s(oundary)g(conditions)g (and)i(with)e(the)118 816 y(constrain)m(t)i(that)g(there)f(are)h(also)f Fu(\006)g FA(crossing)g(surfaces)g(in)f Fv(R)2273 771 y Fs(i;)p Ft(\006)2272 844 y Fs(N)2396 816 y Fu(\\)20 b Fv(Q)2549 783 y Fs(i)2549 843 y(N)2616 816 y FA(\()2661 780 y Fs(\016)r(h)p 2661 795 75 4 v 2681 847 a Fx(4)2745 816 y Fv(N)10 b FA(\).)218 1031 y(F)-8 b(or)32 b(simplicit)m(y)-8 b(,)29 b(let)i(us)g(de\014ne)f(the)i(new)f(constrained)f(partition)g (function)g(on)h(the)h(domain)e(\003)3569 998 y Fs(\016)3569 1058 y(N)3636 1031 y FA(.)118 1139 y(Let)h Fu(S)38 b FA(b)s(e)30 b(the)h(ev)m(en)m(t)h(suc)m(h)e(that)h(there)g(exist)g(t)m (w)m(o)h(crossing)e(surfaces)g(of)h(go)s(o)s(d)f Fv(H)7 b FA(-blo)s(c)m(ks.)42 b(F)-8 b(or)31 b(an)m(y)118 1247 y(spin)c(con\014guration)i(in)f Fu(S)7 b FA(,)30 b(the)f(surface)h(of)f (+)g(blo)s(c)m(ks)g(included)d(in)i Fu(f)p Fv(i)e Fu(2)f FA(\003)2737 1214 y Fs(\016)2737 1274 y(N)2820 1247 y Fu(j)15 b FA(0)26 b Fr(6)f Fv(i)3058 1261 y Fx(1)3123 1247 y Fr(6)3229 1212 y Fs(\016)p 3229 1227 36 4 v 3229 1279 a Fx(4)3274 1247 y Fv(N)10 b Fu(g)30 b FA(whic)m(h)118 1360 y(is)37 b(the)i(closest)f(to)h Fu(f)p Fv(i)873 1374 y Fx(1)952 1360 y FA(=)f(0)p Fu(g)h FA(is)e(denoted)h(b)m(y)g Fu(S)1836 1327 y Fx(+)1895 1360 y FA(.)64 b(In)38 b(the)g(same)h(w)m(a) m(y)-8 b(,)41 b(the)e(surface)f(of)g Fu(\000)g FA(blo)s(c)m(ks)118 1473 y(included)29 b(in)i Fu(f)p Fv(i)e Fu(2)e FA(\003)847 1440 y Fs(\016)847 1500 y(N)930 1473 y Fu(j)36 b(\000)1094 1437 y Fs(\016)p 1093 1452 V 1093 1504 a Fx(4)1138 1473 y Fv(N)i Fr(6)28 b Fv(i)1379 1487 y Fx(1)1447 1473 y Fr(6)f FA(0)p Fu(g)33 b FA(whic)m(h)e(is)g(the)h(closest)g(to)h Fu(f)p Fv(i)2660 1487 y Fx(1)2728 1473 y FA(=)28 b(0)p Fu(g)k FA(is)f(denoted)h(b)m(y)g Fu(S)3577 1440 y Ft(\000)3636 1473 y FA(.)118 1592 y(The)27 b(constrained)h(partition)e(function)h (with)f(mixed)h(b)s(oundary)f(conditions)g(\()p Fv(\033)2917 1559 y Fx(+)2977 1592 y Fv(;)15 b(\033)3072 1559 y Ft(\000)3131 1592 y FA(\))26 b Fu(2)f Fv(G)3349 1559 y Ft(\006)p Fs(;")3460 1592 y FA(\(\003)3558 1559 y Fs(\016)3558 1619 y(N)3626 1592 y FA(\))118 1700 y(is)30 b(de\014ned)f(b)m(y)818 1887 y Fv(Z)887 1843 y Fs(\033)929 1819 y Fm(+)980 1843 y Fs(;\033)1042 1819 y Fl(\000)880 1928 y Fs(\015)t(;)p Fx(\003)989 1905 y Fp(\016)989 1951 y(N)1099 1887 y FA(\()p Fu(S)7 b FA(\))25 b(=)1352 1801 y Fq(X)1397 1991 y Fs(\033)1499 1887 y FA(1)1544 1901 y Ft(S)1596 1887 y FA(\()p Fv(\033)s FA(\))15 b(exp)1891 1813 y Fq(\000)1933 1887 y Fu(\000)p Fv(\014)5 b(H)2136 1901 y Fs(\015)2180 1813 y Fq(\000)2221 1887 y Fv(\033)s Fu(j)15 b FA(\()p Fv(\033)2406 1849 y Fx(+)2467 1887 y Fv(;)g(\033)2562 1849 y Ft(\000)2621 1887 y FA(\))2656 1813 y Fq(\001\001)2770 1887 y Fv(:)118 2139 y FA(The)33 b(constrain)m(t)h Fu(S)40 b FA(implies)30 b(that)k(the)g(mesoscopic)g(in)m(terface)g(is)e(lo)s(calized)g(inside)f (the)j(strip)s(e)e Fu(f)p Fv(i)f Fu(2)118 2252 y FA(\003)181 2219 y Fs(\016)181 2279 y(N)264 2252 y Fu(j)e(j)p Fv(i)374 2266 y Fx(1)414 2252 y Fu(j)h Fr(6)580 2216 y Fs(\016)p 579 2231 V 579 2283 a Fx(4)624 2252 y Fv(N)10 b Fu(g)p FA(.)48 b(Th)m(us,)33 b(uniformly)d(o)m(v)m(er)k(the)f(b)s(oundary)e (conditions)g(in)h Fv(G)2886 2219 y Ft(\006)p Fs(;")2997 2252 y FA(\(\003)3095 2219 y Fs(\016)3095 2279 y(N)3163 2252 y FA(\))h(the)g(system)118 2360 y(will)28 b(relax)i(to)h (equilibrium)26 b(in)j(eac)m(h)i(region)f(outside)g(this)f(strip)s(e.) 118 2535 y FF(Prop)s(osition)41 b(4.2.)j Fn(L)-5 b(et)36 b Fv(\014)h(>)31 b FA(1)37 b Fn(and)g(\014x)f Fv(\015)1682 2550 y Fs(\014)1761 2535 y Fv(>)31 b FA(0)p Fn(,)38 b Fv(")32 b(>)f FA(0)36 b Fn(such)h(that)g(the)g(The)-5 b(or)g(ems)38 b(4.1)f(and)g(4.2)118 2643 y(hold.)43 b(Then,)33 b(for)g(al)5 b(l)34 b Fv(\015)c(<)25 b(\015)1111 2658 y Fs(\014)1158 2643 y Fn(,)774 2939 y FA(lim)767 3001 y Fs(\016)r Ft(!)p Fx(0)922 2939 y FA(lim)15 b(sup)959 3018 y Fs(N)7 b Ft(!1)1309 2878 y FA(1)p 1225 2919 214 4 v 1225 3002 a Fv(N)1308 2976 y Fs(d)p Ft(\000)p Fx(1)1499 2939 y FA(sup)1464 3023 y Fs(\033)1506 3004 y Fm(+)1557 3023 y Fs(;\033)1619 3004 y Fl(\000)1687 2939 y FA(log)1820 2757 y Fq(0)1820 2920 y(@)1909 2840 y Fv(Z)1978 2796 y Fs(\033)2020 2772 y Fm(+)2071 2796 y Fs(;\033)2133 2772 y Fl(\000)1971 2881 y Fx(\003)2020 2858 y Fp(\016)2020 2904 y(N)2190 2840 y FA(\()p Fu(S)g FA(\))p 1909 2919 414 4 v 1975 3024 a Fv(Z)2044 2980 y Fs(\033)2086 2961 y Fm(+)2137 2980 y Fs(;)t Fx(~)-39 b Fs(\033)2199 2961 y Fl(\000)2037 3065 y Fx(\003)2086 3042 y Fp(\016)2086 3088 y(N)2332 2757 y Fq(1)2332 2920 y(A)2452 2939 y Fr(6)45 b Fu(\000)20 b Fv(\034)2699 2954 y Fs(\014)s(;\015)2821 2939 y Fv(;)629 b FA(\(4.9\))118 3231 y Fn(wher)-5 b(e)36 b(the)f(supr)-5 b(emum)36 b(is)e(taken)h(over)g(the)g(b)-5 b(oundary)37 b(c)-5 b(on\014gur)g(ations)37 b(such)e(that)h FA(\()p Fv(\033)3136 3198 y Fx(+)3195 3231 y Fv(;)15 b(\033)3290 3198 y Ft(\000)3350 3231 y FA(\))35 b Fn(b)-5 b(elong)118 3341 y(to)33 b Fv(G)298 3308 y Ft(\006)p Fs(;")410 3341 y FA(\(\003)508 3308 y Fs(\016)508 3368 y(N)576 3341 y FA(\))p Fn(.)118 3517 y(Pr)-5 b(o)g(of.)43 b FA(As)34 b(b)s(efore,)i(the)e(pro)s(of)g(is)g(based)g(up)s(on)f(an)h (in)m(terp)s(olation)f(whic)m(h)g(enables)h(us)g(to)h(compare)118 3625 y(the)j(statistically)e(pure)h(b)s(oundary)e(conditions)h(with)g (the)i(mixed)e(b)s(oundary)g(conditions)f(\(1)p Fv(;)15 b Fu(\000)p FA(1\).)118 3733 y(Nev)m(ertheless,)34 b(the)f(metho)s(d)g (is)e(quite)i(di\013eren)m(t)f(b)s(ecause)h(it)f(relies)f(on)i(the)g (relaxation)f(of)h(the)g(spin)118 3841 y(con\014gurations)d(in)f(the)h (domains)f(outside)h(the)h(strip)s(e)d Fu(f)p Fv(i)15 b Fu(j)27 b(j)p Fv(i)2251 3855 y Fx(1)2291 3841 y Fu(j)e Fr(6)2448 3805 y Fs(\016)p 2447 3820 36 4 v 2447 3872 a Fx(4)2493 3841 y Fv(N)10 b Fu(g)p FA(.)41 b(Notice)31 b(that)435 4101 y(lim)15 b(sup)472 4179 y Fs(N)7 b Ft(!1)822 4040 y FA(1)p 738 4080 214 4 v 738 4164 a Fv(N)821 4137 y Fs(d)p Ft(\000)p Fx(1)977 4101 y FA(log)1109 3946 y Fq( )1191 4037 y Fv(Z)1260 3993 y Fx(+)p Fs(;)p Ft(\000)1253 4066 y Fs(N)1393 4037 y FA(\()p Fu(S)g FA(\))p 1191 4080 335 4 v 1257 4175 a Fv(Z)1326 4131 y Fx(+)p Fs(;)p Fx(+)1319 4204 y Fs(N)1536 3946 y Fq(!)1648 4101 y Fr(6)40 b FA(lim)15 b(sup)1796 4179 y Fs(N)7 b Ft(!1)2147 4040 y FA(1)p 2063 4080 214 4 v 2063 4164 a Fv(N)2146 4137 y Fs(d)p Ft(\000)p Fx(1)2301 4101 y FA(log)2434 3946 y Fq( )2516 4037 y Fv(Z)2585 3993 y Fx(+)p Fs(;)p Ft(\000)2578 4066 y Fs(N)p 2516 4080 203 4 v 2516 4175 a Fv(Z)2585 4131 y Fx(+)p Fs(;)p Fx(+)2578 4204 y Fs(N)2728 3946 y Fq(!)2825 4101 y FA(=)25 b Fu(\000)p Fv(\034)3032 4116 y Fs(\014)s(;\015)3154 4101 y Fv(:)218 4348 y FA(W)-8 b(e)31 b(de\014ne)f(2)h(regions)1067 4567 y Fu(B)1130 4530 y Fx(+)1271 4567 y FA(=)1425 4439 y Fq(\032)1493 4567 y Fv(i;)107 b(i)1687 4581 y Fx(1)1752 4567 y Fu(2)25 b FA([)1874 4506 y Fv(\016)p 1873 4546 46 4 v 1873 4630 a FA(2)1929 4567 y Fv(N)5 b(;)2058 4506 y(\016)p 2057 4546 V 2057 4630 a FA(2)2112 4567 y Fv(N)30 b FA(+)2316 4506 y(10)p 2316 4546 91 4 v 2336 4630 a Fv(\015)2417 4567 y FA(])2442 4439 y Fq(\033)2541 4567 y Fv(;)1067 4821 y Fu(B)1130 4783 y Ft(\000)1271 4821 y FA(=)1425 4693 y Fq(\032)1493 4821 y Fv(i;)107 b(i)1687 4835 y Fx(1)1752 4821 y Fu(2)25 b FA([)p Fu(\000)1945 4759 y Fv(\016)p 1944 4800 46 4 v 1944 4883 a FA(2)1999 4821 y Fv(N)30 b Fu(\000)2203 4759 y FA(10)p 2203 4800 91 4 v 2223 4883 a Fv(\015)2304 4821 y(;)15 b Fu(\000)2426 4759 y Fv(\016)p 2425 4800 46 4 v 2425 4883 a FA(2)2481 4821 y Fv(N)10 b FA(])2589 4693 y Fq(\033)2687 4821 y Fv(:)118 5050 y FA(The)37 b(spins)e(con\014gurations)h(inside)f(\()p Fu(B)1503 5017 y Fx(+)1562 5050 y Fv(;)15 b Fu(B)1665 5017 y Ft(\000)1724 5050 y FA(\))37 b(are)g(in)m(terp)s(olated)f(b)m(y) h(the)h(constan)m(t)g(con\014guration)118 5158 y(\()p Fv(m)233 5125 y Ft(\003)273 5158 y Fv(;)15 b Fu(\000)p Fv(m)464 5125 y Ft(\003)503 5158 y FA(\))850 5328 y Fu(8)p Fv(s)24 b Fu(2)h FA([0)p Fv(;)15 b FA(1])p Fv(;)g Fu(8)p Fv(i)27 b Fu(2)e(B)1532 5291 y Fx(+)1591 5328 y Fv(;)197 b(\033)1865 5342 y Fs(i)1893 5328 y FA(\()p Fv(s)p FA(\))84 b(=)e Fv(s\033)2338 5342 y Fs(i)2386 5328 y FA(+)20 b(\(1)h Fu(\000)f Fv(s)p FA(\))p Fv(m)2827 5291 y Ft(\003)2827 5352 y Fs(\014)2889 5328 y Fv(;)1276 5477 y Fu(8)p Fv(i)25 b Fu(2)g(B)1532 5440 y Ft(\000)1591 5477 y Fv(;)197 b(\033)1865 5491 y Fs(i)1893 5477 y FA(\()p Fv(s)p FA(\))84 b(=)e Fv(s\033)2338 5491 y Fs(i)2386 5477 y Fu(\000)20 b FA(\(1)h Fu(\000)f Fv(s)p FA(\))p Fv(m)2827 5440 y Ft(\003)2827 5501 y Fs(\014)2889 5477 y Fv(:)p eop %%Page: 26 26 26 25 bop 118 45 a Fx(26)1460 b(T.)23 b(BODINEA)n(U)118 383 y FA(Outside)43 b(\()p Fu(B)569 350 y Fx(+)627 383 y Fv(;)15 b Fu(B)730 350 y Ft(\000)789 383 y FA(\),)48 b(the)c(spins)e(are)i(unc)m(hanged.)81 b(Let)45 b Fv(Z)2248 339 y Fs(\033)2290 315 y Fm(+)2341 339 y Fs(;\033)2403 315 y Fl(\000)2241 412 y Fs(N)s(;s)2459 383 y FA(\()p Fu(S)7 b FA(\))45 b(b)s(e)e(the)h(partition)f(function)118 501 y(dep)s(ending)29 b(on)i(the)g(spins)e Fv(\033)s FA(\()p Fv(s)p FA(\).)44 b(The)30 b(con\014gurations)h(of)g(the)g (partition)f(function)g(in)g(the)h(denomi-)118 609 y(nator)26 b(are)h(in)m(terp)s(olated)e(in)f(\()p Fu(B)1209 576 y Fx(+)1268 609 y Fv(;)15 b Fu(B)1371 576 y Ft(\000)1430 609 y FA(\))26 b(with)f(the)h(con\014guration)f(\()p Fv(m)2507 576 y Ft(\003)2507 637 y Fs(\014)2554 609 y Fv(;)15 b(m)2674 576 y Ft(\003)2674 637 y Fs(\014)2722 609 y FA(\))26 b(and)f(the)h(corresp)s(onding)118 757 y(partition)j(function)g(is)h(denoted)g(b)m(y)g Fv(Z)1483 713 y Fs(\033)1525 690 y Fm(+)1576 713 y Fs(;)t Fx(~)-39 b Fs(\033)1638 690 y Fl(\000)1476 786 y Fs(N)s(;s)1695 757 y FA(.)218 886 y(F)-8 b(or)31 b(giv)m(en)f(b)s(oundary)f (conditions)f(\()p Fv(\033)1552 853 y Fx(+)1612 886 y Fv(;)15 b(\033)1707 853 y Ft(\000)1767 886 y FA(\))25 b Fu(2)g Fv(G)1984 853 y Ft(\006)p Fs(;")2096 886 y FA(\(\003)2194 853 y Fs(\016)2194 913 y(N)2262 886 y FA(\),)30 b(w)m(e)h(in)m(tro)s (duce)1054 1166 y(\010\()p Fv(s)p FA(\))26 b(=)f(log)1497 1089 y Fv(Z)1566 1045 y Fx(+)p Fs(;)p Ft(\000)1559 1118 y Fs(N)s(;s)1699 1089 y FA(\()p Fu(S)7 b FA(\))p 1497 1145 335 4 v 1563 1241 a Fv(Z)1632 1196 y Fx(+)p Fs(;)p Fx(+)1625 1269 y Fs(N)s(;s)1862 1166 y Fu(\000)20 b FA(log)2095 1089 y Fv(Z)2164 1045 y Fs(\033)2206 1022 y Fm(+)2257 1045 y Fs(;\033)2319 1022 y Fl(\000)2157 1118 y Fs(N)s(;s)2376 1089 y FA(\()p Fu(S)7 b FA(\))p 2095 1145 414 4 v 2162 1251 a Fv(Z)2231 1207 y Fs(\033)2273 1188 y Fm(+)2324 1207 y Fs(;)t Fx(~)-39 b Fs(\033)2386 1188 y Fl(\000)2224 1280 y Fs(N)s(;s)2534 1166 y Fv(:)870 b FA(\(4.10\))218 1443 y(When)38 b Fv(s)f FA(=)h(0,)j(the)d(spin)e(con\014gurations)i(in) f Fu(B)1927 1410 y Fx(+)2023 1443 y FA(and)h Fu(B)2271 1410 y Ft(\000)2367 1443 y FA(decouple)g(the)g(con\014gurations)f(in)m (to)118 1550 y(three)31 b(indep)s(enden)m(t)d(systems.)143 1808 y(\010\(0\))e(=)f(log)579 1653 y Fq( )661 1744 y Fv(Z)730 1700 y Fx(+)p Fs(;m)867 1677 y Fl(\003)723 1773 y Fs(N)p 661 1787 246 4 v 661 1885 a Fv(Z)730 1840 y Fx(+)p Fs(;m)867 1822 y Fl(\003)723 1913 y Fs(N)942 1744 y Fv(Z)1011 1700 y Fs(m)1073 1677 y Fl(\003)1109 1700 y Fs(;)p Ft(\000)p Fs(m)1246 1677 y Fl(\003)1004 1773 y Fs(N)1286 1744 y FA(\()p Fu(S)7 b FA(\))p 942 1787 477 4 v 1035 1885 a Fv(Z)1104 1840 y Fs(m)1166 1822 y Fl(\003)1202 1840 y Fs(;m)1284 1822 y Fl(\003)1097 1913 y Fs(N)1453 1744 y Fv(Z)1522 1700 y Ft(\000)p Fs(m)1639 1677 y Fl(\003)1675 1700 y Fs(;)p Ft(\000)1515 1773 y Fs(N)p 1453 1787 301 4 v 1481 1885 a Fv(Z)1550 1840 y Fs(m)1612 1822 y Fl(\003)1648 1840 y Fs(;)p Fx(+)1543 1913 y Fs(N)1764 1653 y Fq(!)1856 1808 y Fu(\000)20 b FA(log)2079 1653 y Fq( )2161 1744 y Fv(Z)2230 1700 y Fs(\033)2272 1677 y Fm(+)2323 1700 y Fs(;m)2405 1677 y Fl(\003)2223 1773 y Fs(N)p 2161 1787 285 4 v 2161 1893 a Fv(Z)2230 1849 y Fs(\033)2272 1830 y Fm(+)2323 1849 y Fs(;m)2405 1830 y Fl(\003)2223 1922 y Fs(N)2481 1744 y Fv(Z)2550 1700 y Fs(m)2612 1677 y Fl(\003)2647 1700 y Fs(;)p Ft(\000)p Fs(m)2784 1677 y Fl(\003)2543 1773 y Fs(N)2825 1744 y FA(\()p Fu(S)7 b FA(\))p 2481 1787 477 4 v 2574 1885 a Fv(Z)2643 1840 y Fs(m)2705 1822 y Fl(\003)2741 1840 y Fs(;m)2823 1822 y Fl(\003)2636 1913 y Fs(N)2992 1744 y Fv(Z)3061 1700 y Ft(\000)p Fs(m)3178 1677 y Fl(\003)3214 1700 y Fs(;\033)3276 1677 y Fl(\000)3054 1773 y Fs(N)p 2992 1787 341 4 v 3020 1893 a Fv(Z)3089 1849 y Fs(m)3151 1830 y Fl(\003)3187 1849 y Fs(;)t Fx(~)-39 b Fs(\033)3249 1830 y Fl(\000)3082 1922 y Fs(N)3343 1653 y Fq(!)3445 1808 y Fv(:)118 2067 y FA(The)30 b(symmetries)g(of)g(the)h (mo)s(del)e(imply)f(the)i(cancellation)g(of)h(all)e(the)i(terms)f (\010\(0\))c(=)f(0.)218 2175 y(All)34 b(what)h(remains)f(to)i(do)f(is)f (to)i(con)m(trol)g(the)f(deriv)-5 b(ativ)m(e)35 b(\010)2367 2142 y Ft(0)2390 2175 y FA(\()p Fv(s)p FA(\).)55 b(W)-8 b(e)37 b(encoun)m(ter)e(t)m(w)m(o)i(t)m(yp)s(es)e(of)118 2283 y(terms)30 b(in)f(the)i(sections)f Fu(B)1036 2250 y Ft(\006)168 2464 y FA(\010)234 2426 y Ft(0)257 2464 y FA(\()p Fv(s)p FA(\))84 b(=)550 2396 y Fq(P)646 2491 y Fs(i)p Ft(2B)765 2472 y Fm(+)815 2491 y Fs(;j)t Ft(2)p Fx(\003)964 2468 y Fp(\016)964 2514 y(N)1055 2464 y Fv(J)1105 2478 y Fs(\015)1150 2464 y FA(\()p Fv(i;)15 b(j)5 b FA(\))1418 2363 y Fq(h\020)1516 2464 y Fv(\026)1571 2420 y Fx(+)p Fs(;)p Ft(\000)1571 2493 y Fs(\014)s(;\015)t(;N)s(;s)1808 2390 y Fq(\000)1850 2464 y Fv(\033)1902 2478 y Fs(j)1939 2464 y FA(\()p Fv(\033)2026 2478 y Fs(i)2074 2464 y Fu(\000)20 b Fv(m)2245 2426 y Ft(\003)2284 2464 y FA(\))p Fu(jS)2406 2390 y Fq(\001)2469 2464 y Fu(\000)g Fv(\026)2615 2420 y Fx(+)p Fs(;)p Fx(+)2615 2493 y Fs(\014)s(;\015)t(;N)s(;s)2852 2390 y Fq(\000)2894 2464 y Fv(\033)2946 2478 y Fs(j)2983 2464 y FA(\()p Fv(\033)3070 2478 y Fs(i)3118 2464 y Fu(\000)g Fv(m)3289 2426 y Ft(\003)3328 2464 y FA(\))3363 2390 y Fq(\001)3405 2363 y(\021)1418 2663 y Fu(\000)1514 2562 y Fq(\020)1568 2663 y Fv(\026)1623 2619 y Fs(\033)1665 2595 y Fm(+)1717 2619 y Fs(;\033)1779 2595 y Fl(\000)1623 2692 y Fs(\014)s(;\015)t(;N)s(;s)1861 2589 y Fq(\000)1903 2663 y Fv(\033)1955 2677 y Fs(j)1991 2663 y FA(\()p Fv(\033)2078 2677 y Fs(i)2127 2663 y Fu(\000)g Fv(m)2298 2625 y Ft(\003)2337 2663 y FA(\))p Fu(jS)2459 2589 y Fq(\001)2522 2663 y Fu(\000)g Fv(\026)2668 2619 y Fs(\033)2710 2595 y Fm(+)2761 2619 y Fs(;)t Fx(~)-39 b Fs(\033)2823 2595 y Fl(\000)2668 2692 y Fs(\014)s(;\015)t(;N)s(;s)2905 2589 y Fq(\000)2947 2663 y Fv(\033)2999 2677 y Fs(j)3035 2663 y FA(\()p Fv(\033)3122 2677 y Fs(i)3171 2663 y Fu(\000)20 b Fv(m)3342 2625 y Ft(\003)3381 2663 y FA(\))3416 2589 y Fq(\001)3458 2562 y(\021)q(i)458 2862 y FA(+)544 2794 y Fq(P)640 2889 y Fs(i)p Ft(2B)759 2870 y Fl(\000)811 2889 y Fs(;j)t Ft(2)p Fx(\003)960 2866 y Fp(\016)960 2912 y(N)1051 2862 y Fv(J)1101 2876 y Fs(\015)1146 2862 y FA(\()p Fv(i;)15 b(j)5 b FA(\))1418 2761 y Fq(h\020)1516 2862 y Fv(\026)1571 2817 y Fx(+)p Fs(;)p Ft(\000)1571 2891 y Fs(\014)s(;\015)t(;N)s(;s)1808 2788 y Fq(\000)1850 2862 y Fv(\033)1902 2876 y Fs(j)1939 2862 y FA(\()p Fv(\033)2026 2876 y Fs(i)2074 2862 y FA(+)20 b Fv(m)2245 2824 y Ft(\003)2284 2862 y FA(\))p Fu(jS)2406 2788 y Fq(\001)2469 2862 y Fu(\000)g Fv(\026)2615 2817 y Fx(+)p Fs(;)p Fx(+)2615 2891 y Fs(\014)s(;\015)t(;N)s(;s)2852 2788 y Fq(\000)2894 2862 y Fv(\033)2946 2876 y Fs(j)2983 2862 y FA(\()p Fv(\033)3070 2876 y Fs(i)3118 2862 y Fu(\000)g Fv(m)3289 2824 y Ft(\003)3328 2862 y FA(\))3363 2788 y Fq(\001)3405 2761 y(\021)1418 3061 y Fu(\000)1514 2960 y Fq(\020)1568 3061 y Fv(\026)1623 3016 y Fs(\033)1665 2993 y Fm(+)1717 3016 y Fs(;\033)1779 2993 y Fl(\000)1623 3090 y Fs(\014)s(;\015)t(;N)s(;s)1861 2987 y Fq(\000)1903 3061 y Fv(\033)1955 3075 y Fs(j)1991 3061 y FA(\()p Fv(\033)2078 3075 y Fs(i)2127 3061 y FA(+)g Fv(m)2298 3023 y Ft(\003)2337 3061 y FA(\))p Fu(jS)2459 2987 y Fq(\001)2522 3061 y Fu(\000)g Fv(\026)2668 3016 y Fs(\033)2710 2993 y Fm(+)2761 3016 y Fs(;)t Fx(~)-39 b Fs(\033)2823 2993 y Fl(\000)2668 3090 y Fs(\014)s(;\015)t(;N)s(;s)2905 2987 y Fq(\000)2947 3061 y Fv(\033)2999 3075 y Fs(j)3035 3061 y FA(\()p Fv(\033)3122 3075 y Fs(i)3171 3061 y Fu(\000)20 b Fv(m)3342 3023 y Ft(\003)3381 3061 y FA(\))3416 2987 y Fq(\001)3458 2960 y(\021)q(i)3586 3061 y Fv(:)218 3265 y FA(By)30 b(using)f(the)i(exp)s (onen)m(tial)e(deca)m(y)j(of)e(correlations)g(\(Theorem)h(4.4\),)h(w)m (e)f(obtain)240 3418 y Fq(X)118 3627 y Fs(i)p Ft(2B)237 3608 y Fm(+)288 3627 y Fs(;j)t Ft(2)p Fx(\003)437 3604 y Fp(\016)437 3650 y(N)524 3505 y Fv(J)574 3519 y Fs(\015)619 3505 y FA(\()p Fv(i;)15 b(j)5 b FA(\))817 3400 y Fq(\014)817 3455 y(\014)817 3509 y(\014)849 3505 y Fv(\026)904 3460 y Fx(+)p Fs(;)p Fx(+)904 3534 y Fs(\014)s(;\015)t(;N)s(;s)1142 3431 y Fq(\000)1184 3505 y Fv(\033)1236 3519 y Fs(j)1272 3505 y FA(\()p Fv(\033)1359 3519 y Fs(i)1408 3505 y Fu(\000)20 b Fv(m)1579 3467 y Ft(\003)1618 3505 y FA(\))1653 3431 y Fq(\001)1715 3505 y Fu(\000)g Fv(\026)1861 3460 y Fs(\033)1903 3437 y Fm(+)1954 3460 y Fs(;)t Fx(~)-39 b Fs(\033)2016 3437 y Fl(\000)1861 3534 y Fs(\014)s(;\015)t(;N)s(;s)2099 3431 y Fq(\000)2141 3505 y Fv(\033)2193 3519 y Fs(j)2229 3505 y FA(\()p Fv(\033)2316 3519 y Fs(i)2365 3505 y Fu(\000)20 b Fv(m)2536 3467 y Ft(\003)2575 3505 y FA(\))2610 3431 y Fq(\001)2652 3400 y(\014)2652 3455 y(\014)2652 3509 y(\014)2723 3505 y Fr(6)2829 3443 y Fv(N)2912 3410 y Fs(d)p Ft(\000)p Fx(1)p 2829 3484 214 4 v 2889 3567 a Fv(\015)2941 3541 y Fs(d)3067 3505 y FA(exp\()p Fu(\000)p Fv(c\015)3403 3467 y Fx(2)3458 3505 y Fv(\016)s(N)10 b FA(\))15 b Fv(:)118 3815 y FA(This)29 b(estimate)i(holds)e(uniformly) e(o)m(v)m(er)32 b(the)e(b)s(oundary)f(conditions)g(\()p Fv(\033)2628 3782 y Fx(+)2687 3815 y Fv(;)20 b FA(~)-50 b Fv(\033)2782 3782 y Ft(\000)2842 3815 y FA(\))25 b Fu(2)g(G)3047 3782 y Fx(+)p Fs(;")3159 3815 y FA(\(\003)3257 3782 y Fs(\016)3257 3842 y(N)3325 3815 y FA(\).)118 4021 y FF(Remark)e(4.3.)34 b Fn(Notic)-5 b(e)23 b(that)i(The)-5 b(or)g(em)25 b(4.4)f(holds)h(also)f(for)g(the)g(interp)-5 b(olate)g(d)26 b(me)-5 b(asur)g(es)25 b FA(\()p Fv(\026)3294 3977 y Fs(\033)3336 3954 y Fm(+)3388 3977 y Fs(;)t Fx(~)-39 b Fs(\033)3450 3954 y Fl(\000)3294 4051 y Fs(\014)s(;\015)t(;N)s(;s) 3532 4021 y FA(\))3567 4040 y Fs(s)p Ft(2)p Fx([0)p Fs(;)p Fx(1])3781 4021 y Fn(.)118 4135 y(This)37 b(fact)f(was)h(p)-5 b(ointe)g(d)38 b(to)f(us)f(by)g(E.)f(Pr)-5 b(esutti.)53 b(The)36 b(interp)-5 b(olation)39 b(by)d(mor)-5 b(e)38 b(r)-5 b(e)g(gular)37 b(c)-5 b(on\014gur)g(a-)118 4243 y(tions)37 b(c)-5 b(an)36 b(only)h(impr)-5 b(ove)37 b(the)g(pr)-5 b(op)g(erties)38 b(of)e(the)g(me)-5 b(asur)g(e,)38 b(thus)f(mo)-5 b(difying)37 b(the)f(inter)-5 b(actions)38 b(on)118 4351 y FA(\()p Fu(B)216 4318 y Fx(+)275 4351 y Fv(;)15 b Fu(B)378 4318 y Ft(\000)437 4351 y FA(\))33 b Fn(do)-5 b(es)34 b(not)f(alter)g(the)g(c)-5 b(onclusion)34 b(of)f(the)g(The)-5 b(or)g(em.)218 4530 y FA(The)22 b(minimal)e(section)i(b)s(ecomes)h (e\013ectiv)m(e)i(in)c(order)h(to)h(estimate)h(the)f(other)g(terms.)38 b(W)-8 b(e)23 b(consider)118 4638 y(the)37 b(spin)d(correlations)i(in)g Fu(B)1152 4605 y Fx(+)1247 4638 y FA(\(the)h(same)f(argumen)m(t)h (holds)e(with)h Fu(B)2612 4605 y Ft(\000)2670 4638 y FA(\).)60 b(Theorem)36 b(4.4)h(pro)m(vides)118 4748 y(estimates)29 b(for)f(b)s(oundary)e(conditions)g(whic)m(h)h(are)h(in)f Fu(G)2062 4715 y Fx(+)p Fs(;")2174 4748 y FA(\(\003)2272 4715 y Fs(\016)2272 4775 y(N)2339 4748 y FA(\))i(and)e(therefore)i (cannot)f(b)s(e)g(applied)118 4857 y(directly)i(for)h(mixed)e(b)s (oundary)g(conditions.)42 b(Nev)m(ertheless)31 b(the)g(section)h Fu(S)2791 4824 y Fx(+)2880 4857 y FA(screens)f(the)h(e\013ect)g(of)118 4965 y(the)27 b Fu(\000)g FA(b)s(oundary)e(conditions.)38 b(Th)m(us)26 b(the)h(con\014gurations)f(in)f Fu(B)2372 4932 y Fx(+)2458 4965 y FA(relax)h(to)i(the)f(+)g(pure)f(phase.)39 b(Let)118 5072 y(\001)194 5034 y Fx(+)194 5101 y Ft(S)286 5072 y FA(b)s(e)32 b(the)i(domain)e(ab)s(o)m(v)m(e)i(the)f(surface)g Fu(S)1688 5039 y Fx(+)1747 5072 y FA(.)49 b(By)34 b(conditioning,)e (wrt)g(the)i(con\014guration)e Fv(\033)3450 5092 y Ft(S)3498 5073 y Fm(+)3586 5072 y FA(in)118 5182 y(the)f(section)f Fu(S)640 5150 y Fx(+)699 5182 y FA(,)h(w)m(e)g(ha)m(v)m(e)647 5397 y Fv(\026)702 5353 y Fx(+)p Fs(;)p Ft(\000)702 5426 y Fs(\014)s(;\015)t(;N)s(;s)940 5323 y Fq(\000)981 5397 y Fv(\033)1033 5411 y Fs(j)1070 5397 y Fv(\033)1122 5411 y Fs(i)1150 5397 y Fu(jS)1237 5323 y Fq(\001)1304 5397 y FA(=)1600 5335 y(1)p 1410 5376 426 4 v 1410 5471 a Fv(\026)1465 5427 y Fx(+)p Fs(;)p Ft(\000)1465 5501 y Fs(\014)s(;\015)t(;N)s(;s)1703 5471 y FA(\()p Fu(S)7 b FA(\))1845 5397 y Fv(\026)1900 5353 y Fx(+)p Fs(;)p Ft(\000)1900 5426 y Fs(\014)s(;\015)t(;N)s(;s)2138 5323 y Fq(\000)2180 5397 y FA(1)2225 5411 y Ft(S)2302 5397 y Fv(\026)2357 5342 y Fx(+)p Fs(;\033)2472 5366 y Fl(S)2514 5352 y Fm(+)2357 5442 y Fs(\014)s(;\015)t(;)p Fx(\001)2539 5412 y Fm(+)2539 5465 y Fl(S)2589 5442 y Fs(;s)2645 5397 y FA(\()p Fv(\033)2732 5411 y Fs(j)2769 5397 y Fv(\033)2821 5411 y Fs(i)2849 5397 y FA(\))2884 5323 y Fq(\001)2941 5397 y Fv(:)p eop %%Page: 27 27 27 26 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(27)118 366 y FA(According)31 b(to)i(Theorem)e (4.4)i(the)e(previous)f(expression)h(can)g(b)s(e)g(replaced)g(b)m(y)h (the)g(exp)s(ectation)g(in)118 474 y(the)f(in\014nite)d(strip)s(e)h Fu(f)p Fv(i;)107 b Fu(j)p Fv(i)1103 488 y Fs(j)1140 474 y Fu(j)25 b Fr(6)g Fv(N)5 b(;)46 b(j)31 b FA(=)25 b(2)p Fv(;)15 b(:)g(:)g(:)i(;)e(d)p Fu(g)p FA(.)118 557 y Fq(\014)118 611 y(\014)118 666 y(\014)148 661 y Fv(\026)203 617 y Fx(+)p Fs(;)p Ft(\000)203 690 y Fs(\014)s(;\015)t(;N)s(;s)441 587 y Fq(\000)483 661 y Fv(\033)535 675 y Fs(j)571 661 y Fv(\033)623 675 y Fs(i)651 661 y Fu(jS)738 587 y Fq(\001)800 661 y Fu(\000)20 b Fv(\026)946 624 y Fs(m)1008 600 y Fl(\003)946 684 y Fs(\014)s(;\015)t(;s)1105 661 y FA(\()p Fv(\033)1192 675 y Fs(j)1229 661 y Fv(\033)1281 675 y Fs(i)1309 661 y FA(\))1344 557 y Fq(\014)1344 611 y(\014)1344 666 y(\014)1415 661 y Fr(6)41 b FA(sup)1527 733 y Fs(\033)1567 757 y Fl(S)1609 743 y Fm(+)1679 557 y Fq(\014)1679 611 y(\014)1679 666 y(\014)1709 661 y Fv(\026)1764 606 y Fx(+)p Fs(;\033)1879 630 y Fl(S)1921 616 y Fm(+)1764 706 y Fs(\014)s(;\015)t(;)p Fx(\001)1946 676 y Fm(+)1946 729 y Fl(S)1996 706 y Fs(;s)2052 587 y Fq(\000)2094 661 y Fv(\033)2146 675 y Fs(j)2182 661 y Fv(\033)2234 675 y Fs(i)2262 587 y Fq(\001)2324 661 y Fu(\000)20 b Fv(\026)2470 624 y Fs(m)2532 600 y Fl(\003)2470 684 y Fs(\014)s(;\015)t(;s)2629 661 y FA(\()p Fv(\033)2716 675 y Fs(j)2753 661 y Fv(\033)2805 675 y Fs(i)2833 661 y FA(\))2868 557 y Fq(\014)2868 611 y(\014)2868 666 y(\014)2939 661 y Fr(6)40 b FA(exp\()p Fu(\000)p Fv(c\015)3386 624 y Fx(2)3426 661 y Fv(\016)s(N)10 b FA(\))15 b Fv(;)118 921 y FA(where)20 b Fv(\026)426 888 y Fs(m)488 864 y Fl(\003)426 948 y Fs(\014)s(;\015)t(;s)605 921 y FA(is)f(the)i(measure)f(on)g(the)h(in\014nite)d(strip)s(e.)36 b(The)19 b(same)i(iden)m(tit)m(y)f(holds)e(for)j Fv(\026)3158 876 y Fs(\033)3200 853 y Fm(+)3251 876 y Fs(;\033)3313 853 y Fl(\000)3158 950 y Fs(\014)s(;\015)t(;N)s(;s)3395 847 y Fq(\000)3437 921 y Fv(\033)3489 935 y Fs(j)3525 921 y Fv(\033)3577 935 y Fs(i)3606 921 y Fu(jS)3693 847 y Fq(\001)3734 921 y FA(,)118 1034 y(therefore)390 1103 y Fq(X)268 1312 y Fs(i)p Ft(2B)387 1293 y Fm(+)438 1312 y Fs(;j)t Ft(2)p Fx(\003)587 1289 y Fp(\016)587 1335 y(N)674 1190 y Fv(J)724 1204 y Fs(\015)769 1190 y FA(\()p Fv(i;)15 b(j)5 b FA(\))952 1112 y Fq(\014)952 1167 y(\014)984 1190 y Fv(\026)1039 1145 y Fx(+)p Fs(;)p Ft(\000)1039 1219 y Fs(\014)s(;\015)t(;N)s(;s)1277 1116 y Fq(\000)1319 1190 y Fv(\033)1371 1204 y Fs(j)1407 1190 y FA(\()p Fv(\033)1494 1204 y Fs(i)1543 1190 y Fu(\000)20 b Fv(m)1714 1152 y Ft(\003)1753 1190 y FA(\))15 b Fu(j)g(S)1905 1116 y Fq(\001)2030 1190 y Fu(\000)83 b Fv(\026)2239 1145 y Fs(\033)2281 1122 y Fm(+)2332 1145 y Fs(;\033)2394 1122 y Fl(\000)2239 1219 y Fs(\014)s(;\015)t(;N)s(;s)2477 1116 y Fq(\000)2519 1190 y Fv(\033)2571 1204 y Fs(j)2607 1190 y FA(\()p Fv(\033)2694 1204 y Fs(i)2743 1190 y Fu(\000)20 b Fv(m)2914 1152 y Ft(\003)2953 1190 y FA(\))15 b Fu(j)g(S)3105 1116 y Fq(\001)3147 1112 y(\014)3147 1167 y(\014)2573 1520 y Fr(6)2679 1459 y Fv(N)2762 1426 y Fs(d)p Ft(\000)p Fx(1)p 2679 1499 214 4 v 2739 1583 a Fv(\015)2791 1556 y Fs(d)2918 1520 y FA(exp\()p Fu(\000)p Fv(c\015)3254 1483 y Fx(2)3309 1520 y Fv(\016)s(N)10 b FA(\))15 b Fv(:)218 1719 y FA(This)28 b(concludes)i(the)g(prop)s(osition.)2125 b Fr(\003)118 1886 y FF(Remark)34 b(4.4.)43 b Fn(The)32 b(pr)-5 b(o)g(of)35 b(of)e(the)-5 b(or)g(em)35 b(4.2)e(do)-5 b(es)34 b(not)f(use)g(c)-5 b(orr)g(elation)35 b(ine)-5 b(qualities.)1280 2097 y FA(5.)46 b Fz(Appendix)33 b(:)45 b(Theorem)34 b(3.1)218 2259 y FA(The)c(pro)s(of)f(of)i(the)f(domination)f(b)s(ound)f(for)j (the)f(0-blo)s(c)m(ks)h(\(3.2\))h(is)d(divided)f(in)m(to)i(3)h(steps.) 118 2475 y Fn(Step)i(1.)p 118 2507 277 4 v 35 w FA(Let)i(us)e(start)i (with)e(a)i(single)e(b)s(o)m(x.)52 b(If)1807 2451 y Fq(b)1802 2475 y Fy(B)1856 2489 y Fs(N)s(;K)2009 2475 y FA(\()p Fv(x)p FA(\))35 b(is)f(not)g(a)h Fn(go)-5 b(o)g(d)36 b FA(b)s(o)m(x)e(then)g(either)g(there)g(is)118 2582 y(a)j(con)m(tour)g(of)g(length)f(at)h(least)g Fv(K)1351 2549 y Fs(\013)1437 2582 y FA(crossing)f(the)g(enlarged)h(b)s(oundary)d (or)j(conditionally)d(on)i(the)118 2690 y(ev)m(en)m(t)28 b(that)f(the)f(b)s(o)m(x)h Fy(B)924 2704 y Fs(K)999 2690 y FA(\()p Fv(x)p FA(\))g(is)e(surrounded)f(b)m(y)i(a)h(surface)f(of)h (spins)d(of)i(sign)g Fv(")2852 2704 y Fs(x)2896 2690 y FA(,)h(the)g(magnetization)118 2798 y Fu(M)227 2812 y Fs(N)s(;K)374 2798 y FA(\()p Fv(x)p FA(\))35 b(is)e(at)m(ypical.)52 b(These)34 b(t)m(w)m(o)h(o)s(ccurrences)f(can)g(b)s(e)g(estimated)g (separately)-8 b(.)53 b(Applying)31 b(the)118 2906 y(P)m(eierls)f (estimate)h(\(2.8\))r(,)f(w)m(e)h(get)537 3068 y Fv(\026)592 3030 y Fx(+)592 3098 y Fs(\014)s(;N)722 2995 y Fq(\000)763 3068 y FA(there)g(is)e(a)i(con)m(tour)g(crossing)f Fv(@)5 b Fy(B)1947 3082 y Fs(K)2021 3068 y FA(\()p Fv(x)p FA(\))2144 2995 y Fq(\001)2211 3068 y Fr(6)25 b Fv(K)2391 3031 y Fs(d)p Ft(\000)p Fx(1)2536 3068 y FA(exp\()p Fu(\000)p Fv(c)2820 3083 y Fs(\014)2868 3068 y Fv(K)2952 3031 y Fs(\013)3001 3068 y FA(\))15 b Fv(:)399 b FA(\(5.1\))118 3229 y(Conditionally)26 b(on)j(the)g(o)s(ccurrence)g(of)h(a)f (connected)h(surface)f Fu(S)36 b FA(of)29 b Fv(")2556 3243 y Fs(x)2600 3229 y FA(-spins)e(surrounding)f(the)j(b)s(o)m(x)118 3337 y Fy(B)173 3351 y Fs(K)247 3337 y FA(\()p Fv(x)p FA(\),)46 b(the)c(con\014gurations)f(inside)e Fy(B)1530 3351 y Fs(K)1604 3337 y FA(\()p Fv(x)p FA(\))j(are)h(decoupled)d(from)i (the)g(exterior.)75 b(W)-8 b(e)43 b(\014rst)e(use)118 3445 y(Tc)m(heb)m(yshev)31 b(inequalit)m(y)207 3705 y Fv(\026)262 3666 y Fx(+)262 3734 y Fs(\014)s(;N)407 3631 y Fq(\000)449 3705 y Fu(fjM)628 3719 y Fs(N)s(;K)776 3705 y FA(\()p Fv(x)p FA(\))21 b Fu(\000)f Fv(")1052 3719 y Fs(x)1096 3705 y Fv(m)1176 3667 y Ft(\003)1215 3705 y Fu(j)26 b Fr(>)f Fv(\020)7 b Fu(g)1484 3627 y Fq(\014)1484 3682 y(\014)1544 3705 y Fu(S)1606 3631 y Fq(\001)1688 3705 y Fr(6)1894 3643 y FA(1)p 1794 3684 246 4 v 1794 3767 a Fv(\020)1841 3741 y Fx(2)1880 3767 y Fv(K)1964 3741 y Fx(2)p Fs(d)2050 3705 y Fv(\026)2105 3665 y Fs(")2138 3673 y Fp(x)2105 3738 y Fs(\014)s(;)p Fx(in)n(t\()p Ft(S)e Fx(\))2373 3522 y Fq(0)2373 3685 y(@)2453 3631 y(\000)2578 3618 y(X)2509 3820 y Fs(i)p Ft(2)p Fo(B)2619 3831 y Fp(K)2683 3820 y Fx(\()p Fs(x)p Fx(\))2793 3705 y Fv(\033)2845 3719 y Fs(i)2894 3705 y Fu(\000)19 b Fv(")3026 3719 y Fs(x)3071 3705 y Fv(m)3151 3667 y Ft(\003)3190 3631 y Fq(\001)3232 3654 y Fx(2)3271 3522 y Fq(1)3271 3685 y(A)3381 3705 y Fv(:)118 3969 y FA(where)25 b(in)m(t\()p Fu(S)7 b FA(\))26 b(is)e(the)i(region)f (surrounded)e(b)m(y)i Fu(S)7 b FA(.)39 b(As)26 b Fu(S)32 b FA(has)25 b(b)s(een)g(c)m(hosen)h(as)g(the)f(closest)h(surface)g(to) 118 4077 y(\()p Fy(B)208 4091 y Fs(K)5 b Fx(+)p Fs(K)393 4072 y Fp(\013)446 4077 y FA(\))481 4044 y Fs(c)516 4077 y FA(,)30 b(the)f(magnetization)h(inside)d(the)j(b)s(o)m(x)f Fy(B)1956 4091 y Fs(K)2031 4077 y FA(\()p Fv(x)p FA(\))h(is)e (measurable)h(after)g(the)h(conditioning)d(.)118 4185 y(As)32 b(a)g(consequence)g(of)g(the)g(P)m(eierls)e(estimates)j(\(lo)m (w)e(temp)s(erature)h(expansions\),)f(the)h(correlations)118 4293 y(deca)m(y)g(exp)s(onen)m(tially)c(in)h(the)i Fv(")1236 4307 y Fs(x)1280 4293 y FA(-pure)f(phase,)g(so)h(that)g(w)m(e)f(obtain) 914 4486 y Fv(\026)969 4447 y Fs(")1002 4455 y Fp(x)969 4519 y Fx(in)n(t)q(\()p Ft(S)5 b Fx(\))1175 4486 y FA(\()q Fu(fjM)1390 4500 y Fs(N)s(;K)1538 4486 y FA(\()p Fv(x)p FA(\))20 b Fu(\000)g Fv(")1813 4500 y Fs(x)1858 4486 y Fv(m)1938 4449 y Ft(\003)1977 4486 y Fu(j)25 b Fr(>)g Fv(\020)7 b Fu(g)p FA(\))26 b Fu(\024)2464 4425 y FA(1)p 2382 4465 211 4 v 2382 4549 a Fv(\020)2429 4522 y Fx(2)2468 4549 y Fv(K)2552 4522 y Fs(d)2602 4486 y Fv(\037)15 b(;)776 b FA(\(5.2\))118 4700 y(where)30 b(the)h(susceptibilit)m(y)c Fv(\037)e FA(=)1267 4632 y Fq(P)1363 4727 y Fs(i)p Ft(2)p Fo(Z)1484 4708 y Fp(d)1534 4700 y Fv(\026)1589 4662 y Fx(+)1589 4730 y Fs(\014)1648 4700 y FA(\()p Fv(\033)1735 4714 y Fx(0)1774 4700 y FA(;)15 b Fv(\033)1866 4714 y Fs(i)1895 4700 y FA(\))31 b(is)e(\014nite.)118 4916 y Fn(Step)k(2.)p 118 4948 277 4 v 31 w FA(In)d(order)f(to)j(ev)-5 b(aluate)31 b(the)f(probabilit)m(y)e(of)j(the)f(ev)m(en)m(t)1203 5011 y Fq(n)1264 5112 y Fv(u)1316 5068 y Fs(\020)1316 5141 y(N)s(;K)1463 5112 y FA(\()p Fv(x)1550 5126 y Fx(1)1590 5112 y FA(\))c(=)f(0)p Fv(;)15 b(:)g(:)g(:)i(;)e(u)2046 5068 y Fs(\020)2046 5141 y(N)s(;K)2193 5112 y FA(\()p Fv(x)2280 5127 y Fs(`)2313 5112 y FA(\))26 b(=)f(0)2515 5011 y Fq(o)118 5324 y FA(the)j(lattice)555 5301 y Fq(b)548 5324 y Fy(D)607 5338 y Fs(N)t(;K)788 5324 y FA(is)f(partionned)g(in)m (to)h Fv(c)1556 5339 y Fs(d)1625 5324 y FA(sub-lattices)f(\()2146 5301 y Fq(b)2138 5324 y Fy(D)2198 5277 y Fx(\()q Fs(i)p Fx(\))2198 5353 y Fs(N)s(;K)2351 5324 y FA(\))2386 5338 y Fs(i)20 b Fd(6)g Fs(c)2536 5350 y Fp(d)2604 5324 y FA(suc)m(h)27 b(that)i(t)m(w)m(o)g(cub)s(es)e(of)h(size)118 5472 y Fv(K)j FA(+)23 b Fv(K)404 5439 y Fs(\013)489 5472 y FA(cen)m(tered)37 b(on)f(t)m(w)m(o)h(sites)e(of)h Fy(D)1542 5424 y Fx(\()p Fs(i)p Fx(\))1542 5501 y Fs(N)s(;K)1731 5472 y FA(are)g(disjoin)m(t.)55 b(By)36 b(applying)e(H\177)-45 b(older)35 b(inequalit)m(y)-8 b(,)36 b(the)p eop %%Page: 28 28 28 27 bop 118 45 a Fx(28)1460 b(T.)23 b(BODINEA)n(U)118 366 y FA(estimate)31 b(\(3.2\))h(is)e(reduced)f(to)j(cub)s(es)d(whic)m (h)g(are)i(not)g(nearest)f(neigh)m(b)s(ors.)183 608 y Fv(\026)238 570 y Fx(+)238 638 y Fs(\014)s(;N)383 507 y Fq(\020)437 608 y Fv(u)489 564 y Fs(\020)489 637 y(N)s(;K)636 608 y FA(\()p Fv(x)723 622 y Fx(1)763 608 y FA(\))25 b(=)g(0)p Fv(;)15 b(:)g(:)g(:)i(;)e(u)1218 564 y Fs(\020)1218 637 y(N)s(;K)1366 608 y FA(\()p Fv(x)1453 623 y Fs(`)1486 608 y FA(\))26 b(=)f(0)1688 507 y Fq(\021)1783 608 y Fr(6)1919 491 y Fs(c)1950 503 y Fp(d)1894 522 y Fq(Y)1895 717 y Fs(i)p Fx(=1)2025 608 y Fv(\026)2080 570 y Fx(+)2080 638 y Fs(\014)s(;N)2225 507 y Fq(\020)2280 608 y Fu(8)p Fv(x)2383 622 y Fs(j)2444 608 y Fu(2)2537 585 y Fq(b)2530 608 y Fy(D)2589 560 y Fx(\()q Fs(i)p Fx(\))2589 637 y Fs(N)s(;K)2742 608 y Fv(;)107 b(u)2926 564 y Fs(\020)2926 637 y(N)s(;K)3073 608 y FA(\()p Fv(x)3160 622 y Fs(j)3197 608 y FA(\))25 b(=)g(0)3398 507 y Fq(\021)3480 503 y Fm(1)p 3463 515 65 3 v 3463 556 a Fp(c)3491 574 y(d)3571 608 y Fv(:)118 895 y Fn(Step)33 b(3.)p 118 927 277 4 v 38 w FA(The)k(ev)m(en)m(t)873 794 y Fq(n)933 895 y Fv(u)985 851 y Fs(\020)985 924 y(N)s(;K)1132 895 y FA(\()p Fv(x)1219 909 y Fx(1)1259 895 y FA(\))26 b(=)f(0)p Fv(;)15 b(:)g(:)g(:)i(;)e(u)1715 851 y Fs(\020)1715 924 y(N)s(;K)1862 895 y FA(\()p Fv(x)1949 910 y Fs(`)1983 895 y FA(\))25 b(=)g(0)2184 794 y Fq(o)2282 895 y FA(can)38 b(b)s(e)f(decomp)s(osed)g (in)m(to)g(2)h(terms)f(:)118 1032 y(on)29 b Fv(`)281 999 y Ft(0)333 1032 y FA(b)s(o)m(xes)g(the)g(densit)m(y)f(is)g(at)m (ypical,)i(whereas)e(there)i(are)f(con)m(tours)g(crossing)g(the)g Fv(`)17 b Fu(\000)g Fv(`)3276 999 y Ft(0)3328 1032 y FA(enlarged)118 1140 y(b)s(oundaries)28 b(of)j(the)f(remaining)f(b)s(o) m(xes.)218 1248 y(F)-8 b(or)31 b(a)g(giv)m(en)f(collection)g(of)h Fv(j)36 b FA(b)s(o)m(xes,)30 b(w)m(e)h(de\014ne)149 1412 y Fu(A)222 1426 y Fs(j)341 1412 y FA(=)83 b Fu(f)p FA(The)30 b Fv(j)36 b FA(b)s(o)m(xes)31 b(are)g(surrounded)c(b)m(y)k Fu(\006)f FA(surfaces,)g(but)g(their)f(a)m(v)m(eraged)k(magnetizations) 677 1547 y(are)e(non)f(t)m(ypical)o Fu(g)162 1682 y(B)222 1696 y Fs(j)341 1682 y FA(=)83 b Fu(f)q FA(There)29 b(are)i(con)m (tours)g(crossing)f(the)g Fv(j)36 b FA(enlarged)30 b(b)s(oundaries)e (of)j(the)f(b)s(o)m(xes)p Fu(g)h Fv(:)218 1846 y FA(The)25 b(probabilities)e(of)k(b)s(oth)e(ev)m(en)m(ts)j(can)e(b)s(e)g(ev)-5 b(aluated)26 b(as)g(follo)m(ws.)39 b(As)26 b(the)g Fv(j)32 b FA(b)s(o)m(xes)26 b(are)h(disjoin)m(t)118 1954 y(and)j(the)g (surfaces)h(of)f(spins)e(decouple)i(the)h(con\014gurations)e(inside)f (eac)m(h)k(b)s(o)m(x)1116 2130 y Fv(\026)1171 2092 y Fx(+)1171 2160 y Fs(\014)s(;N)1301 2130 y FA(\()p Fu(A)1409 2144 y Fs(j)1445 2130 y FA(\))26 b Fr(6)1602 2057 y Fq(\000)1644 2130 y Fv(\026)1699 2092 y Fx(+)1699 2160 y Fs(\014)s(;N)1828 2130 y FA(\()p Fu(A)1936 2144 y Fx(1)1976 2130 y FA(\))2011 2057 y Fq(\001)2053 2079 y Fs(j)2114 2130 y Fr(6)2210 2057 y Fq(\000)2252 2130 y Fv(\013)2310 2144 y Fs(K)2379 2057 y Fq(\001)2420 2079 y Fs(j)2472 2130 y Fv(;)118 2306 y FA(where)k(the)h(constan)m(t)g Fv(\013)962 2320 y Fs(K)1056 2306 y FA(=)1225 2265 y Fs(\037)p 1162 2285 171 4 v 1162 2343 a(\020)1198 2324 y Fm(2)1232 2343 y Fs(K)1297 2324 y Fp(d)1373 2306 y FA(w)m(as)f(in)m(tro)s(duced)f(in)g (\(5.2\))r(.)357 2650 y Fv(\026)412 2612 y Fx(+)412 2679 y Fs(\014)s(;N)542 2650 y FA(\()p Fu(B)637 2664 y Fs(j)674 2650 y FA(\))c(=)880 2531 y Fs(j)830 2563 y Fq(X)839 2759 y Fs(i)p Fx(=1)977 2650 y Fv(\026)1032 2612 y Fx(+)1032 2679 y Fs(\014)s(;N)1161 2576 y Fq(\000)1203 2650 y Fu(f9)30 b Fv(i)h FA(con)m(tours)g(crossing)f(the)g Fv(j)36 b FA(enlarged)30 b(b)s(oundaries)m Fu(g)3173 2576 y Fq(\001)3231 2650 y Fv(:)118 2895 y FA(W)-8 b(e)32 b(c)m(ho)s(ose)f Fv(i)g FA(blo)s(c)m(ks)e(as)i(starting)f(p)s(oin)m(ts)f(of)i(these)g (con)m(tours.)41 b(Then)29 b(w)m(e)i(ha)m(v)m(e)h(to)f(ev)-5 b(aluate)1394 2986 y Fq(X)1144 3187 y Ft(j)p Fx(\000)1208 3196 y Fm(1)1242 3187 y Ft(j)p Fx(+)p Ft(\001\001\001)o Fx(+)p Ft(j)p Fx(\000)1495 3197 y Fp(i)1521 3187 y Ft(j)19 b Fd(>)g Fs(j)t(K)1732 3169 y Fp(\013)1790 3073 y Fv(\026)1845 3034 y Fx(+)1845 3102 y Fs(\014)s(;N)1975 3073 y FA(\(\000)2067 3087 y Fx(1)2107 3073 y Fv(;)c(:)g(:)g(:)h(;)f FA(\000)2365 3087 y Fs(i)2394 3073 y FA(\))g Fv(;)118 3346 y FA(where)30 b(the)h(con)m(tours)f(\(\000)996 3360 y Fx(1)1036 3346 y Fv(;)15 b(:)g(:)g(:)i(;)e FA(\000)1295 3360 y Fs(i)1323 3346 y FA(\))31 b(ha)m(v)m(e)g(also)g(to)g(cross)f(eac)m(h)i(b)s (oundaries)c(of)i(the)h Fv(j)36 b FA(cub)s(es.)218 3453 y(Let)31 b Fv(n)436 3467 y Fs(r)503 3453 y FA(b)s(e)f(the)h(n)m(um)m(b) s(er)e(of)h(b)s(oundaries)e(crossed)j(b)m(y)f(the)g(con)m(tour)i Fv(r)662 3544 y Fq(X)412 3746 y Ft(j)p Fx(\000)476 3755 y Fm(1)511 3746 y Ft(j)p Fx(+)p Ft(\001\001\001)n Fx(+)p Ft(j)p Fx(\000)763 3756 y Fp(i)789 3746 y Ft(j)19 b Fd(>)h Fs(j)t(K)1001 3727 y Fp(\013)1058 3631 y Fv(\026)1113 3592 y Fx(+)1113 3660 y Fs(\014)s(;N)1243 3631 y FA(\(\000)1335 3645 y Fx(1)1375 3631 y Fv(;)15 b(:)g(:)g(:)h(;)f FA(\000)1633 3645 y Fs(i)1662 3631 y FA(\))25 b Fr(6)1969 3544 y Fq(X)1833 3740 y Fs(n)1876 3749 y Fm(1)1911 3740 y Fx(+)p Ft(\001\001\001)o Fx(+)p Fs(n)2123 3750 y Fp(i)2149 3740 y Fx(=)p Fs(j)2326 3544 y Fq(X)2276 3746 y Fx(\(\000)2347 3754 y Fp(r)2382 3746 y Fs(;n)2445 3754 y Fp(r)2480 3746 y Fx(\))2522 3631 y Fv(\026)2577 3592 y Fx(+)2577 3660 y Fs(\014)s(;N)2707 3631 y FA(\(\000)2799 3645 y Fx(1)2838 3631 y Fv(;)15 b(:)g(:)g(:)i(;)e FA(\000)3097 3645 y Fs(i)3125 3631 y FA(\))g Fv(:)118 3904 y FA(If)28 b(a)g(con)m(tour)g(crosses)h Fv(n)961 3918 y Fs(r)1026 3904 y FA(b)s(oundaries)d(then)h(it)h(has)f (a)i(length)e(at)i(least)f Fv(n)2662 3918 y Fs(r)2699 3904 y Fv(K)2783 3871 y Fs(\013)2848 3904 y FA(+)15 b(\()p Fv(n)3024 3918 y Fs(r)3077 3904 y Fu(\000)g FA(1\))p Fv(K)35 b FA(b)s(ecause)118 4012 y(the)c(distance)f(b)s(et)m(w)m(een)h (the)f(b)s(o)m(xes)h(is)e(at)i(least)g Fv(K)7 b FA(.)40 b(Th)m(us)478 4156 y Fq(X)229 4357 y Ft(j)p Fx(\000)293 4366 y Fm(1)327 4357 y Ft(j)p Fx(+)p Ft(\001\001\001)n Fx(+)p Ft(j)p Fx(\000)579 4367 y Fp(i)605 4357 y Ft(j)19 b Fd(>)h Fs(j)t(K)817 4338 y Fp(\013)875 4242 y Fv(\026)930 4204 y Fx(+)930 4272 y Fs(\014)s(;N)1059 4242 y FA(\(\000)1151 4256 y Fx(1)1191 4242 y Fv(;)15 b(:)g(:)g(:)i(;)e FA(\000)1450 4256 y Fs(i)1478 4242 y FA(\))109 b Fr(6)1936 4156 y Fq(X)1801 4351 y Fs(n)1844 4360 y Fm(1)1878 4351 y Fx(+)p Ft(\001\001\001)o Fx(+)p Fs(n)2090 4361 y Fp(i)2116 4351 y Fx(=)p Fs(j)2268 4129 y(i)2222 4156 y Fq(Y)2218 4350 y Fs(r)r Fx(=1)2357 4242 y FA(exp\()p Fu(\000)p Fv(c)2641 4257 y Fs(\014)2689 4242 y Fv(n)2744 4256 y Fs(r)2781 4242 y Fv(K)2865 4205 y Fs(\013)2935 4242 y Fu(\000)20 b Fv(c)3065 4257 y Fs(\014)3112 4242 y FA(\()p Fv(n)3202 4256 y Fs(r)3260 4242 y Fu(\000)g FA(1\))p Fv(K)7 b FA(\))1622 4595 y Fr(6)108 b FA(exp)o(\()p Fu(\000)p Fv(c)2084 4610 y Fs(\014)2132 4595 y Fv(j)5 b(K)2258 4557 y Fs(\013)2308 4595 y FA(\))2358 4440 y Fq( )2462 4481 y Ft(1)2431 4509 y Fq(X)2430 4703 y Fs(n)p Fx(=1)2578 4595 y FA(exp\()p Fu(\000)p Fv(c)2862 4610 y Fs(\014)2910 4595 y FA(\()p Fv(n)20 b Fu(\000)g FA(1\))p Fv(K)7 b FA(\))3310 4440 y Fq(!)3383 4462 y Fs(i)1622 4829 y Fr(6)108 b Fv(C)1873 4791 y Fs(i)1931 4829 y FA(exp)o(\()p Fu(\000)p Fv(c)2214 4844 y Fs(\014)2262 4829 y Fv(j)5 b(K)2388 4791 y Fs(\013)2438 4829 y FA(\))15 b Fv(:)118 5228 y(\026)173 5190 y Fx(+)173 5257 y Fs(\014)s(;N)303 5228 y FA(\()p Fu(B)398 5242 y Fs(j)434 5228 y FA(\))26 b Fr(6)656 5110 y Fs(j)606 5142 y Fq(X)615 5337 y Fs(i)p Fx(=1)752 5100 y Fq(\022)819 5167 y Fv(j)825 5291 y(i)862 5100 y Fq(\023)929 5228 y Fv(K)1013 5191 y Fx(\()p Fs(d)p Ft(\000)p Fx(1\))p Fs(i)1222 5228 y Fv(C)1294 5191 y Fs(i)1337 5228 y FA(exp\()p Fu(\000)p Fv(c)1621 5243 y Fs(\014)1668 5228 y Fv(j)5 b(K)1794 5191 y Fs(\013)1844 5228 y FA(\))26 b Fr(6)40 b FA(exp\()p Fu(\000)p Fv(c)2300 5243 y Fs(\014)2363 5228 y Fv(j)5 b(K)2489 5191 y Fs(\013)2538 5228 y FA(\)\(1)22 b(+)e Fv(C)7 b(K)2922 5191 y Fs(d)p Ft(\000)p Fx(1)3052 5228 y FA(\))3087 5191 y Fs(j)3149 5228 y FA(=)25 b(\()p Fv(\013)3338 5191 y Ft(0)3338 5251 y Fs(K)3407 5228 y FA(\))3442 5191 y Fs(j)3494 5228 y Fv(:)118 5480 y FA(where)30 b(the)h(constan)m(t)g Fv(\013)962 5447 y Ft(0)962 5507 y Fs(K)1061 5480 y FA(v)-5 b(anishes)29 b(as)i Fv(K)37 b FA(go)s(es)31 b(to)g(in\014nit)m(y)-8 b(.)p eop %%Page: 29 29 29 28 bop 935 45 a Fx(PHASE)31 b(COEXISTENCE)g(F)n(OR)f(THE)g(KA)n(C)h (ISING)g(MODELS)747 b(29)218 366 y FA(Com)m(bining)28 b(b)s(oth)i(estimates,)h(w)m(e)g(obtain)118 605 y Fv(\026)173 567 y Fx(+)173 635 y Fs(\014)s(;N)318 504 y Fq(\020)372 605 y Fv(u)424 561 y Fs(\020)424 634 y(N)s(;K)571 605 y FA(\()p Fv(x)658 619 y Fx(1)698 605 y FA(\))26 b(=)f(0)p Fv(;)15 b(:)g(:)g(:)i(u)1114 561 y Fs(\020)1114 634 y(N)s(;K)1261 605 y FA(\()p Fv(x)1348 620 y Fs(`)1381 605 y FA(\))26 b(=)f(0)1583 504 y Fq(\021)1678 605 y Fr(6)1845 492 y Fs(`)1794 519 y Fq(X)1789 717 y Fs(`)1818 698 y Fl(0)1840 717 y Fx(=1)1946 477 y Fq(\022)2024 544 y Fv(`)2012 668 y(`)2050 641 y Ft(0)2074 477 y Fq(\023)2156 605 y Fv(\026)2211 567 y Fx(+)2211 635 y Fs(\014)s(;N)2340 605 y FA(\()p Fu(A)2448 621 y Fs(`)2477 602 y Fl(0)2504 605 y FA(\))2539 568 y Fx(1)p Fs(=)p Fx(2)2649 605 y Fv(\026)2704 567 y Fx(+)2704 635 y Fs(\014)s(;N)2834 605 y FA(\()p Fu(B)2929 621 y Fs(`)p Ft(\000)p Fs(`)3042 602 y Fl(0)3068 605 y FA(\))3103 568 y Fx(1)p Fs(=)p Fx(2)3238 605 y Fr(6)3334 532 y Fq(\000)3376 605 y Fv(\013)3434 619 y Fs(K)3523 605 y FA(+)20 b Fv(\013)3672 568 y Ft(0)3672 628 y Fs(K)3740 532 y Fq(\001)3782 554 y Fs(`)3830 605 y Fv(:)118 842 y FA(This)29 b(completes)h(the)h(pro)s(of.)1625 1043 y Fz(References)118 1188 y FE([Al])39 b(K.)33 b(Alexander,)i Fw(Cub)l(e-R)l(o)l(ot)i(Boundary)f(Fluctuations)g(for)f(Dr)l(oplets)h (in)e(R)l(andom)h(Cluster)h(Mo)l(dels)6 b FE(,)36 b Fw(pr)l(eprint)276 1279 y FE(\(2000\).)118 1371 y([AlBe])k(G.)22 b(Alb)r(erti,)h(G.)f (Bellettini,)i Fw(Asymptotic)i(b)l(ehavior)f(of)e(a)h(non)h(lo)l(c)l (al)e(anisotr)l(opic)j(mo)l(del)e(for)g(phase)h(tr)l(ansition)6 b FE(,)276 1462 y Fw(J.)27 b(Math.)h(A)n(nn.)p FE(,)e Fc(310)p FE(,)g(No.)g(3,)g(527-560,)i(\(1998\).)118 1553 y([ABCP])40 b(G.)32 b(Alb)r(erti,)g(G.)g(Bellettini,)i(M.)e(Cassandro,) j(E.)c(Presutti,)j Fw(Surfac)l(e)f(tension)h(in)e(Ising)g(system)i (with)f(Kac)276 1645 y(p)l(otentials)6 b FE(,)28 b(J.)e(Stat.)g(Ph)n (ys.)f Fc(82)p FE(,)i(743{796)h(\(1996\).)118 1736 y([A)n(CC])40 b(K.)22 b(Alexander,)i(J.T.)g(Cha)n(y)n(es,)g(L.)f(Cha)n(y)n(es,)h Fw(The)i(Wul\013)e(c)l(onstruction)j(and)f(asymptotics)h(of)e(the)g (\014nite)h(cluster)276 1827 y(distribution)j(for)e(the)i (two{dimensional)f(Bernoul)t(li)f(p)l(er)l(c)l(olation)6 b FE(,)28 b(Comm.)c(Math.)j(Ph)n(ys.)e Fc(131)p FE(,)i(1{50)g (\(1990\).)118 1919 y([BCP])40 b(G.)27 b(Bellettini,)g(M.)g(Cassandro,) h(E.)e(Presutti,)h Fw(Constr)l(aine)l(d)j(minima)c(of)i(non)g(lo)l(c)l (al)g(fr)l(e)l(e)g(ener)l(gy)h(functionals)6 b FE(,)276 2010 y(J.)26 b(Stat.)g(Ph)n(ys.)g Fc(84)p FE(,)g(1337{1349)j(\(1996\).) 118 2101 y([BBBP])41 b(O.)23 b(Benois,)j(T.)e(Bo)r(dineau,)h(P)-6 b(.)24 b(Butta,)g(E.)g(Presutti,)h Fw(On)g(the)i(validity)e(of)h(van)g (der)g(Waals)g(the)l(ory)h(of)e(surfac)l(e)276 2193 y(tension)6 b FE(,)27 b(Mark.)f(Pro)r(c.)h(and)e(Rel.)h(Fields)h Fc(3)p FE(,)f(175{198)i(\(1997\).)118 2284 y([BBP])40 b(O.)24 b(Benois,)h(T.)f(Bo)r(dineau,)h(E.)f(Presutti,)g Fw(L)l(ar)l(ge)j(deviations)f(in)f(the)i(van)e(der)i(Waals)e(limit)7 b FE(,)23 b(Sto)r(c)n(h.)g(Pro)r(c.)i(and)276 2375 y(Appl.)g Fc(75)p FE(,)h(89{104)i(\(1998\).)118 2467 y([B1])40 b(T.)27 b(Bo)r(dineau,)g Fw(The)h(Wul\013)g(c)l(onstruction)i(in)e(thr) l(e)l(e)i(and)e(mor)l(e)h(dimensions)6 b FE(,)27 b(Comm.)e(Math.)i(Ph)n (ys.)f Fc(207)p FE(,)h(197{)276 2558 y(229)g(\(1999\).)118 2649 y([B2])40 b(T.)26 b(Bo)r(dineau,)h Fw(A)h(micr)l(osc)l(opic)g (derivation)h(of)e(3D)g(e)l(quilibrium)g(crystal)i(shap)l(es)6 b FE(,)28 b(ICMP)f(pro)r(ceedings)f(\(2000\).)118 2741 y([BIV1])39 b(T.)29 b(Bo)r(dineau,)g(D.)f(Io\013e,)h(Y.)e(V)-6 b(elenik,)28 b Fw(R)n(igor)l(ous)j(pr)l(ob)l(abilistic)f(analysis)g(of) f(e)l(quilibrium)g(crystal)i(shap)l(es)6 b FE(,)31 b(J.)276 2832 y(Math.)26 b(Ph)n(ys.)g Fc(41)p FE(,)g(No.3,)h(1033{1098)i (\(2000\).)118 2923 y([BIV2])39 b(T.)21 b(Bo)r(dineau,)h(D.)f(Io\013e,) g(Y.)f(V)-6 b(elenik,)21 b(Win)n(terb)r(ottom)e(construction)i(for)g (\014nite)f(range)g(ferromagnetic)h(mo)r(dels)276 3015 y(:)34 b(a)26 b Fb(L)440 2983 y Fm(1)480 3015 y FE(-approac)n(h,)g (preprin)n(t)e(\(2000\).)118 3106 y([BZ])39 b(A.)25 b(Bo)n(vier,)g(M.)g (Zahradnik,)f Fw(The)j(low-temp)l(er)l(atur)l(e)i(phase)f(of)e(Kac)g (Ising)g(mo)l(dels)6 b FE(,)26 b(J.)f(Stat.)f(Ph)n(ys.)g Fc(87)p FE(,)h(No.1-2,)276 3197 y(311{332)j(\(1997\).)118 3289 y([BMP])40 b(P)-6 b(.)25 b(Butt\022)-38 b(a,)25 b(I.)g(Merola,)i(E.)e(Presutti,)h Fw(On)g(the)i(validity)e(of)g(the)i (van)f(der)g(Waals)g(the)l(ory)h(in)e(Ising)h(systems)h(with)276 3380 y(long)g(r)l(ange)g(inter)l(actions)6 b FE(,)28 b(Mark.)f(Pro)r(c.)g(and)e(Rel.)h(Fields)g Fc(3)p FE(,)h(No.1,)f(63{88) i(\(1997\).)118 3471 y([CCK])40 b(J.)35 b(Cha)n(y)n(es,)i(L.)e(Cha)n(y) n(es,)i(R.)e(Kotec)n(k)q(\023)-39 b(y)33 b(:)53 b Fw(The)36 b(analysis)g(of)f(the)i(Widom-R)l(ow)t(linson)e(mo)l(del)h(by)g(sto)l (chastic)276 3563 y(ge)l(ometric)29 b(metho)l(ds)6 b FE(,)27 b(Comm.)e(Math.)i(Ph)n(ys.)e Fc(172)p FE(,)i(No.3,)f(551{569)j (\(1995\).)118 3654 y([CaPr])40 b(M.)33 b(Cassandro,)j(E.)d(Presutti,)i Fw(Phase)f(tr)l(ansitions)i(in)d(Ising)g(systems)j(with)d(long)h(but)g (\014nite)h(r)l(ange)6 b FE(,)35 b(Mark.)276 3745 y(Pro)r(c.)27 b(and)e(Rel.)h(Fields)h Fc(2)p FE(,)f(241{262)i(\(1996\).)118 3836 y([Ce])40 b(R.)25 b(Cerf,)i Fw(L)l(ar)l(ge)i(deviations)g(for)e (thr)l(e)l(e)j(dimensional)d(sup)l(er)l(critic)l(al)i(p)l(er)l(c)l (olation)6 b FE(,)28 b(Ast)n(\023)-36 b(erisque)25 b Fc(267)h FE(\(2000\).)118 3928 y([CePi1])41 b(R.)25 b(Cerf,)i(A.)f (Pisztora,)h Fw(On)h(the)g(Wul\013)f(crystal)i(in)e(the)i(Ising)e(mo)l (del)8 b FE(,)26 b(to)f(app)r(ear)i(in)e(Ann.)g(Prob)h(\(2000\).)118 4019 y([CePi2])41 b(R.)25 b(Cerf,)i(A.)f(Pisztora,)h Fw(Phase)i(c)l(o)l(existenc)l(e)h(in)d(Ising,)g(Potts)i(and)f(p)l(er)l (c)l(olation)h(mo)l(dels)6 b FE(,)27 b(Preprin)n(t)e(\(2000\).)118 4110 y([DOPT1])40 b(A.)32 b(De)g(Masi,)k(E.)d(Orlandi,)i(E.)e (Presutti,)i(L.)e(T)-6 b(riolo,)36 b Fw(Stability)e(of)g(the)g (interfac)l(e)h(in)f(a)g(mo)l(del)g(of)f(phase)276 4202 y(sep)l(ar)l(ation)6 b FE(,)28 b(Pro)r(ceedings)f(Ro)n(y)n(al)f(So)r (c.)g(Edin)n(burgh)f Fc(124A)p FE(,)h(1013{1022)j(\(1994\).)118 4293 y([DOPT2])40 b(A.)27 b(De)g(Masi,)i(E.)f(Orlandi,)g(E.)g (Presutti,)g(L.)f(T)-6 b(riolo,)30 b Fw(Uniqueness)g(and)g(glob)l(al)f (stability)g(of)g(the)h(instanton)276 4384 y(in)d(non)h(lo)l(c)l(al)f (evolution)i(e)l(quations)6 b FE(,)28 b(Rendicon)n(ti)d(di)g (Matematica)i Fc(14)p FE(,)f(693{723)j(\(1994\).)118 4476 y([DH])38 b(R.L.)33 b(Dobrushin)f(and)h(O.)g(Hryniv,)g Fw(Fluctuations)j(of)e(the)g(phase)i(b)l(oundary)g(in)d(the)i(2D)f (Ising)g(ferr)l(omagnet)7 b FE(,)276 4567 y(Comm.)25 b(Math.)h(Ph)n(ys.)g Fc(189)p FE(,)g(395{445)i(\(1997\).)118 4658 y([DKS])38 b(R.L.)21 b(Dobrushin,)g(R.)f(Kotec)n(k)q(\023)-39 b(y,)21 b(S.)f(Shlosman,)h Fw(Wul\013)h(c)l(onstruction:)35 b(a)23 b(glob)l(al)g(shap)l(e)g(fr)l(om)g(lo)l(c)l(al)g(inter)l(action) 6 b FE(,)276 4750 y(AMS)25 b(translations)i(series,)h(v)n(ol)d(104,)i (Pro)n(vidence)f(R.I.)g(\(1992\).)118 4841 y([DS])38 b(R.L.)33 b(Dobrushin)f(and)g(S.)g(Shlosman,)h Fw(L)l(ar)l(ge)i(and)g (mo)l(der)l(ate)g(deviations)g(in)e(the)i(Ising)e(mo)l(del)8 b FE(,)34 b(Adv)l(ances)d(in)276 4932 y(So)n(viet)25 b(Math.)i Fc(20)p FE(,)f(91{220)i(\(1994\).)118 5024 y([EG])40 b(L.)21 b(Ev)l(ans,)h(R.)f(Gariep)n(y)-6 b(,)22 b Fw(Me)l(asur)l(e)j(The)l(ory)g(and)f(Fine)f(Pr)l(op)l(erties)i(of)e (F)-6 b(unctions)6 b FE(,)24 b(CR)n(C)e(Press,)h(London)e(\(1992\).)118 5115 y([F])66 b(I.)26 b(F)-6 b(onseca,)26 b Fw(The)i(Wul\013)f(the)l (or)l(em)i(r)l(evisite)l(d)8 b FE(,)27 b(Pro)r(c.Ro)n(y)n(al)g(London)e (So)r(c.)i(Sect.)e(A,)h Fc(432)p FE(,)g(125-145)i(\(1991\).)118 5206 y([FM])40 b(I.)28 b(F)-6 b(onseca,)31 b(S.)d(Mueller,)j Fw(A)f(uniqueness)i(pr)l(o)l(of)e(of)g(the)h(Wul\013)f(The)l(or)l(em)6 b FE(,)30 b(Pro)r(c.)g(Ro)n(y)-6 b(.)28 b(So)r(c.)h(Edin)n(burgh;)h (Sect)276 5298 y(A,)25 b Fc(119)p FE(,)i(125{136)h(\(1991\).)118 5389 y([GLM])40 b(G.)30 b(Giacomin,)i(J.)f(Leb)r(o)n(witz,)i(C.)e (Maes,)h Fw(A)l(gr)l(e)l(ement)i(p)l(er)l(c)l(olation)f(and)f(phase)h (c)l(o)l(existenc)l(e)h(in)e(some)g(Gibbs)276 5480 y(systems.)p FE(,)27 b(J.)g(Stat.)e(Ph)n(ys.)h Fc(80)p FE(,)g(No)g(5-6,)g(1379{1403) j(\(1995\).)p eop %%Page: 30 30 30 29 bop 118 45 a Fx(30)1460 b(T.)23 b(BODINEA)n(U)118 366 y FE([I1])50 b(D.)26 b(Io\013e,)g Fw(L)l(ar)l(ge)i(deviations)h (for)f(the)g(2D)g(Ising)f(mo)l(del)h(:)34 b(a)28 b(lower)g(b)l(ound)g (without)h(cluster)g(exp)l(ansions)6 b FE(,)28 b(J.)e(Stat.)276 458 y(Ph)n(ys.)g Fc(74)p FE(,)g(411{432)i(\(1994\).)118 549 y([I2])50 b(D.)22 b(Io\013e,)i Fw(Exact)i(deviation)f(b)l(ounds)h (up)f(to)h FC(T)1598 557 y Fp(c)1654 549 y Fw(for)f(the)g(Ising)g(mo)l (del)f(in)g(two)i(dimensions)6 b FE(,)24 b(Prob.)f(Th.)g(Rel.)g(Fields) 276 640 y Fc(102)p FE(,)k(313{330)h(\(1995\).)118 732 y([ISc])39 b(D.)26 b(Io\013e,)i(R.)e(Sc)n(honmann,)g Fw(Dobrushin-Kote)l(ck)o(\023)-38 b(y-Shlosman)33 b(the)l(ory)d(up)f (to)g(the)g(critic)l(al)g(temp)l(er)l(atur)l(e)6 b FE(,)30 b(Comm.)276 823 y(Math.)c(Ph)n(ys.)g Fc(199)p FE(,)g(117{167)j (\(1998\).)118 914 y([LMP])40 b(J.)28 b(Leb)r(o)n(witz,)g(Mazel,)h (Presutti,)f Fw(Liquid-vap)l(or)j(phase)f(tr)l(ansitions)g(for)f (systems)i(with)e(\014nite-r)l(ange)i(inter)l(ac-)276 1006 y(tions.)p FE(,)26 b(J.)h(Stat.)e(Ph)n(ys.)h Fc(94)p FE(,)g(No.5-6,)h(955{1025)i(\(1999\).)118 1097 y([MMR])39 b(A.)19 b(Messager,)j(S.)d(Miracle-Sol)n(\023)-36 b(e,)22 b(J.)d(Ruiz,)h Fw(Surfac)l(e)i(tension,)h(step)g(fr)l(e)l(e)e(ener)l (gy)i(and)e(fac)l(ets)h(in)f(the)h(e)l(quilibrium)276 1188 y(crystal)8 b FE(,)27 b(J.)f(Stat.)g(Ph)n(ys.)g Fc(79)p FE(,)g(\(1995\).)118 1280 y([MMRS])39 b(A.)26 b(Messager,)j(S.)d(Miracle-Sol)n(\023)-36 b(e,)28 b(J.)f(Ruiz,)f(S.)g (Shlosman,)g Fw(Interfac)l(es)j(in)f(the)h(Potts)g(mo)l(del.)f(II.)e(A) n(ntonov's)276 1371 y(rule)i(and)g(rigidity)f(of)h(the)g(or)l(der)h (disor)l(der)g(interfac)l(e)p FE(,)e(Comm.)e(Math.)h(Ph)n(ys.)f Fc(140)p FE(,)i(No.2,)g(275{290)h(\(1991\).)118 1462 y([Pf)6 b(])40 b(C.E.)28 b(P\014ster,)h Fw(L)l(ar)l(ge)h(deviations)g (and)g(phase)g(sep)l(ar)l(ation)h(in)e(the)h(two)g(dimensional)f(Ising) f(mo)l(del)8 b FE(,)28 b(Helv.)f(Ph)n(ys.)276 1554 y(Acta)f Fc(64)p FE(,)g(953{1054)j(\(1991\).)118 1645 y([PV1])39 b(C.-E.)31 b(P\014ster,)g(Y.)e(V)-6 b(elenik,)30 b Fw(Mathematic)l(al)i (the)l(ory)h(of)e(the)g(wetting)i(phenomenon)f(in)f(the)g(2D)h(Ising)e (mo)l(del)8 b FE(,)276 1736 y(Helv.)26 b(Ph)n(ys.)f(Acta)h Fc(69)p FE(,)g(949-973)i(\(1996\).)118 1828 y([PV2])39 b(C.-E.)30 b(P\014ster,)g(Y)57 b(V)-6 b(elenik,)30 b Fw(L)l(ar)l(ge)h(deviations)h(and)f(c)l(ontinuum)g(limit)e(in)h(the)h (2D)g(Ising)f(mo)l(del)8 b FE(,)30 b(Prob.)f(Th.)276 1919 y(Rel.)d(Fields)g Fc(109)p FE(,)h(435{506)h(\(1997\).)118 2010 y([Pi])43 b(A.)35 b(Pisztora,)k Fw(Surfac)l(e)e(or)l(der)g(lar)l (ge)g(deviations)g(of)f(Ising,)h(Potts)h(and)e(p)l(er)l(c)l(olation)i (mo)l(dels)6 b FE(,)38 b(Prob.)e(Th.)f(Rel.)276 2102 y(Fields)26 b Fc(104)p FE(,)h(427{466)h(\(1996\).)118 2193 y([Sc])39 b(R.H.)28 b(Sc)n(honmann,)g Fw(Se)l(c)l(ond)k(or)l(der)f (lar)l(ge)h(deviation)f(estimates)h(for)e(ferr)l(omagnetic)i(systems)g (in)e(the)h(phase)g(c)l(o-)276 2284 y(existenc)l(e)f(r)l(e)l(gion)6 b FE(,)26 b(Comm.)f(Math.)h(Ph)n(ys.)g Fc(112)p FE(,)g(No.3,)h(409{422) h(\(1987\).)118 2376 y([ScS1])39 b(R.H.)d(Sc)n(honmann,)h(S.)g (Shlosman,)h Fw(Complete)g(analyticity)g(for)g(the)g(2d)f(Ising)h(mo)l (del)f(c)l(omplete)l(d)8 b FE(,)40 b(Comm.)276 2467 y(Math.)26 b(Ph)n(ys.)g Fc(170)p FE(,)g(453{482)j(\(1996\).)118 2558 y([T)-6 b(a])40 b(J.)26 b(T)-6 b(a)n(ylor,)27 b Fw(Crystal)t(line)h(variational)g(pr)l(oblems)6 b FE(,)27 b(Bull.)g(Am.)d(Math.)i(So)r(c.)h Fc(84)p FE(,)f(568{588)i(\(1978\).) 218 2729 y FD(Labora)-5 b(toire)34 b(de)g(Pr)n(obabilit)1254 2723 y(\023)1254 2729 y(es)h(et)f(Mod)1653 2723 y(\022)1653 2729 y(eles)g(Al)1942 2723 y(\023)1942 2729 y(ea)-5 b(toires,)36 b(CNRS-UMR)d(7599,)j(Universit)3390 2723 y(\023)3390 2729 y(e)d(P)-7 b(aris)118 2821 y(VI)28 b(et)h(VI)r(I,)f(UFR)g(de)g(Ma) -5 b(th)1051 2815 y(\023)1051 2821 y(ema)g(tiques,)27 b(case)h(7012,)h(2)g(pla)n(ce)f(Jussieu,)g(P)-7 b(aris)29 b(75251,)g(France.)218 2912 y Fw(E-mail)e(addr)l(ess)6 b FE(:)36 b Fa(bodineau@gauss.math.jussieu.)q(fr)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0101260434298--