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%%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
%%Title: Euler-BGRS.dvi
%%CreationDate: Wed Mar 12 09:18:15 2003
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%DVIPSWebPage: (www.radicaleye.com)
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%+ Euler-BGRS
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% Euler fonts were designed by Hermann Zapf.
% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (EUFM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
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/FontName /EUFM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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/FontBBox{-26 -224 1055 741}readonly def
/UniqueXX 5031986 def
currentdict end
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cleartomark

%%EndFont
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50

% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 76 /L put
dup 86 /V put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
/UniqueXX 5032014 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 182 /acute put
dup 51 /three put
dup 67 /C put
dup 69 /E put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 123 /endash put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueXX 5000795 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 167 /plusminus put
dup 180 /equivalence put
dup 182 /reflexsuperset put
dup 183 /lessequal put
dup 184 /greaterequal put
dup 188 /approxequal put
dup 189 /propersubset put
dup 194 /follows put
dup 195 /arrowleft put
dup 33 /arrowright put
dup 41 /arrowdblright put
dup 49 /infinity put
dup 50 /element put
dup 51 /owner put
dup 54 /negationslash put
dup 57 /existential put
dup 59 /emptyset put
dup 78 /N put
dup 90 /Z put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 107 /bardbl put
dup 110 /backslash put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueXX 5000820 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 167 /Sigma put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 180 /eta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 39 /phi1 put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 64 /partialdiff put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 71 /G put
dup 76 /L put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 88 /X put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 115 /s put
dup 116 /t put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueXX 5087386 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /parenleftbig put
dup 162 /parenrightbig put
dup 163 /bracketleftbig put
dup 164 /bracketrightbig put
dup 167 /ceilingleftbig put
dup 169 /braceleftbig put
dup 170 /bracerightbig put
dup 174 /angbracketrightbig put
dup 175 /vextendsingle put
dup 176 /vextenddouble put
dup 177 /slashbig put
dup 179 /parenleftBig put
dup 180 /parenrightBig put
dup 181 /parenleftbigg put
dup 182 /parenrightbigg put
dup 183 /bracketleftbigg put
dup 184 /bracketrightbigg put
dup 185 /floorleftbigg put
dup 186 /floorrightbigg put
dup 188 /ceilingrightbigg put
dup 189 /braceleftbigg put
dup 190 /bracerightbigg put
dup 191 /angbracketleftbigg put
dup 192 /angbracketrightbigg put
dup 193 /slashbigg put
dup 194 /backslashbigg put
dup 195 /parenleftBigg put
dup 56 /bracelefttp put
dup 57 /bracerighttp put
dup 58 /braceleftbt put
dup 59 /bracerightbt put
dup 60 /braceleftmid put
dup 61 /bracerightmid put
dup 62 /braceex put
dup 63 /arrowvertex put
dup 80 /summationtext put
dup 81 /producttext put
dup 88 /summationdisplay put
dup 89 /productdisplay put
dup 98 /hatwide put
dup 121 /arrowbt put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueXX 5000774 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 73 /I put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueXX 5000769 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37

% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /lessornotequal put
dup 162 /greaterornotequal put
dup 163 /notlessequal put
dup 164 /notgreaterequal put
dup 167 /notprecedes put
dup 169 /lessornotdbleql put
dup 170 /greaterornotdbleql put
dup 174 /notgreaterorslnteql put
dup 175 /lessnotequal put
dup 176 /greaternotequal put
dup 177 /notprecedesoreql put
dup 179 /precedeornoteqvlnt put
dup 180 /followornoteqvlnt put
dup 181 /lessornotsimilar put
dup 182 /greaterornotsimilar put
dup 183 /notlessdblequal put
dup 184 /notgreaterdblequal put
dup 185 /precedenotslnteql put
dup 186 /follownotslnteql put
dup 188 /follownotdbleqv put
dup 189 /lessnotdblequal put
dup 190 /greaternotdblequal put
dup 191 /notsimilar put
dup 192 /notapproxequal put
dup 193 /upslope put
dup 194 /downslope put
dup 195 /notsubsetoreql put
dup 76 /L put
dup 82 /R put
dup 86 /V put
dup 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueXX 5031982 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 163 /multiply put
dup 164 /asteriskmath put
dup 167 /plusminus put
dup 169 /circleplus put
dup 170 /circleminus put
dup 174 /circledivide put
dup 175 /circledot put
dup 176 /circlecopyrt put
dup 177 /openbullet put
dup 179 /equivasymptotic put
dup 180 /equivalence put
dup 181 /reflexsubset put
dup 182 /reflexsuperset put
dup 183 /lessequal put
dup 184 /greaterequal put
dup 185 /precedesequal put
dup 186 /followsequal put
dup 188 /approxequal put
dup 189 /propersubset put
dup 190 /propersuperset put
dup 191 /lessmuch put
dup 192 /greatermuch put
dup 193 /precedes put
dup 194 /follows put
dup 195 /arrowleft put
dup 48 /prime put
dup 107 /bardbl put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueXX 5000816 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 86 /V put
dup 100 /d put
dup 105 /i put
dup 110 /n put
dup 112 /p put
dup 116 /t put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueXX 5087381 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 40 /parenleft put
dup 41 /parenright put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueXX 5000789 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 163 /multiply put
dup 164 /asteriskmath put
dup 167 /plusminus put
dup 169 /circleplus put
dup 170 /circleminus put
dup 174 /circledivide put
dup 175 /circledot put
dup 176 /circlecopyrt put
dup 177 /openbullet put
dup 179 /equivasymptotic put
dup 180 /equivalence put
dup 181 /reflexsubset put
dup 182 /reflexsuperset put
dup 183 /lessequal put
dup 184 /greaterequal put
dup 185 /precedesequal put
dup 186 /followsequal put
dup 188 /approxequal put
dup 189 /propersubset put
dup 190 /propersuperset put
dup 191 /lessmuch put
dup 192 /greatermuch put
dup 193 /precedes put
dup 194 /follows put
dup 195 /arrowleft put
dup 33 /arrowright put
dup 48 /prime put
dup 50 /element put
dup 51 /owner put
dup 54 /negationslash put
dup 59 /emptyset put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 107 /bardbl put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueXX 5000818 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 58 /period put
dup 59 /comma put
dup 61 /slash put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 78 /N put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 88 /X put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 105 /i put
dup 106 /j put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 115 /s put
dup 116 /t put
dup 119 /w put
dup 120 /x put
dup 122 /z put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueXX 5087383 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 73 /I put
dup 83 /S put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 98 /b put
dup 99 /c put
dup 102 /f put
dup 110 /n put
dup 112 /p put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 126 /tilde put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueXX 5000791 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 45 /hyphen put
dup 46 /period put
dup 64 /at put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueXX 5000828 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueXX 5000790 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 89 /Y put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 126 /tilde put
dup 196 /dieresis put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueXX 5000794 def
currentdict end
currentfile eexec
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%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /arrowup put
dup 175 /arrowdown put
dup 176 /quotesingle put
dup 177 /exclamdown put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 58 /colon put
dup 65 /A put
dup 75 /K put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 119 /w put
dup 121 /y put
dup 196 /dieresis put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueXX 5000772 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 196 /dieresis put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
/UniqueXX 5000829 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 167 /Sigma put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 38 /ampersand put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 123 /endash put
dup 196 /dieresis put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueXX 5000793 def
currentdict end
currentfile eexec
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Fu(x;)221 b(y)48 b(;)221 b(z)59 b(;)221 b(t)p Fx(])4317
62279 y(is)434 b(the)f(set)h(of)g(b)36 b(onds)433 b Fr(fh)p
Fu(xy)48 b Fr(i)p Fu(;)221 b Fr(h)p Fu(y)48 b(z)59 b
Fr(i)p Fu(;)221 b Fr(h)p Fu(z)59 b(t)p Fr(i)p Fu(;)221
b Fr(h)p Fu(tx)p Fr(ig)o Fx(.)6268 64482 y(With)447 b(this)f(structure)
g(the)g(lattice)i(b)36 b(ecomes)446 b(a)i(cell-complex)f
Ft(L)391 b Fx(=)g Fr(f)q Ft(L)41950 64681 y Fs(0)42475
64482 y Fu(;)221 b Ft(L)43943 64681 y Fs(1)44469 64482
y Fu(;)g Ft(L)45937 64681 y Fs(2)46463 64482 y Fr(g)p
Fx(,)4317 66087 y(where)451 b Ft(L)8978 66286 y Fs(0)9902
66087 y Fx(=)398 b Ft(Z)12198 65605 y Fs(2)13175 66087
y Fx(is)451 b(the)f(set)h(of)h(sites,)k Ft(L)24478 66286
y Fs(1)25454 66087 y Fx(is)451 b(the)g(set)g(of)g(b)36
b(onds)450 b(and)h Ft(L)39834 66286 y Fs(2)40810 66087
y Fx(is)h(the)e(set)h(of)25578 70015 y(3)p eop
%%Page: 4 4
4 3 bop 4317 7306 a Fx(plaquettes)430 b(\(see)f(e.g.)h([D)-36
b(W)q(]\).)577 b(More)429 b(generally)-108 b(,)432 b(the)c(elemen)-36
b(ts)429 b(of)h Ft(L)39060 7505 y Fq(p)40018 7306 y Fx(will)h(b)36
b(e)429 b(called)4317 8911 y Fu(p)p Fx({cells.)579 b(W)-108
b(e)434 b(also)h(in)-36 b(tro)36 b(duce)432 b(the)h(co{b)36
b(oundary)434 b Fu(\261)50 b(x)369 b Fx(=)g Fr(fh)p Fu(xy)48
b Fr(i)368 b(2)g Ft(L)38294 9110 y Fs(1)39189 8911 y
Fx(:)h Fu(y)417 b Fr(2)368 b Ft(L)43110 9110 y Fs(0)43636
8911 y Fr(g)p Fx(.)6268 11087 y(T)-108 b(o)359 b(a)f(set)g(of)h(b)36
b(onds)358 b Fu(X)474 b Fr(\275)369 b Ft(L)20044 11286
y Fs(1)20927 11087 y Fx(w)-36 b(e)359 b(asso)36 b(ciate)360
b(the)d(sub)36 b(complex)359 b(\244\()p Fu(X)104 b Fx(\))358
b Fr(\275)369 b Ft(L)358 b Fx(de\257ned)4317 12692 y(as)424
b(the)f(maximal)h(closed)g(sub)36 b(complex)423 b(that)g(con)-36
b(tains)424 b Fu(X)528 b Fx(:)573 b(this)423 b(sub)36
b(complex)423 b(is)h(the)4317 14297 y(union)433 b(\244\()p
Fu(X)104 b Fx(\))369 b(=)g(\244)13681 14496 y Fs(0)14207
14297 y Fx(\()p Fu(X)104 b Fx(\))295 b Fr([)g Fx(\244)18781
14496 y Fs(1)19307 14297 y Fx(\()p Fu(X)104 b Fx(\))295
b Fr([)g Fx(\244)23881 14496 y Fs(2)24407 14297 y Fx(\()p
Fu(X)104 b Fx(\))434 b(where)22624 17039 y(\244)23527
17238 y Fs(1)24053 17039 y Fx(\()p Fu(X)104 b Fx(\))369
b(=)g Fu(X)4317 19782 y Fx(is)434 b(the)f(set)h(of)g(b)36
b(onds)433 b(itself,)17209 22524 y(\244)18112 22723 y
Fs(0)18637 22524 y Fx(\()p Fu(X)104 b Fx(\))370 b(=)f
Fr(f)p Fu(x)g Fr(2)f Ft(L)26495 22723 y Fs(0)27390 22524
y Fx(:)h Fu(x)295 b Fr(\\)g Fu(X)474 b Fr(6)p Fx(=)369
b Fr(;g)4317 25267 y Fx(is)434 b(the)f(set)h(of)g(sites)g(whic)-36
b(h)433 b(are)h(endp)36 b(oin)-36 b(ts)432 b(of)j(b)36
b(onds)432 b(of)j Fu(X)104 b Fx(,)434 b(and)9873 28009
y(\244)10776 28208 y Fs(2)11302 28009 y Fx(\()p Fu(X)104
b Fx(\))369 b(=)g Fr(f)p Fu(p)g Fx(=)f([)p Fu(x;)221
b(y)48 b(;)221 b(z)59 b(;)221 b(t)p Fx(])372 b Fr(2)d
Ft(L)25848 28208 y Fs(2)26742 28009 y Fx(:)g Fr(h)p Fu(xy)48
b Fr(i)p Fu(;)221 b Fr(h)p Fu(y)48 b(z)59 b Fr(i)p Fu(;)221
b Fr(h)p Fu(z)59 b(t)p Fr(i)p Fu(;)221 b Fr(h)p Fu(tx)p
Fr(i)368 b(2)h Fu(X)104 b Fr(g)4317 30752 y Fx(is)486
b(the)f(set)h(of)g(plaquettes)f(whose)h(all)h(four)f(b)36
b(ounds)484 b(in)h(their)h(b)36 b(oundary)485 b(b)36
b(elongs)485 b(to)4317 32357 y Fu(X)104 b Fx(.)760 b(Figure)494
b(1)g(sho)-36 b(ws)494 b(a)g(cell)h(complex)f(\244\()p
Fu(X)104 b Fx(\))495 b(asso)36 b(ciated)494 b(to)g(a)h(giv)-36
b(en)494 b(set)g(of)g(b)36 b(onds)4317 33962 y Fu(X)104
b Fx(.)4317 53342 y @beginspecial 59 @llx 535 @lly 552
@urx 769 @ury 3401 @rwi @setspecial
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%!PS-Adobe-3.0
%%Creator: Adobe Illustrator(TM) 7.0
%%For: (--- - cpt) (cnrs)
%%Title: (config.eps)
%%CreationDate: (4/19/02) (3:53 PM)
%%BoundingBox: 59 535 552 769
%%HiResBoundingBox: 59.005 535.1883 551.1486 768.3935
%%DocumentProcessColors: Cyan Magenta Black
%%DocumentSuppliedResources: procset Adobe_level2_AI5 1.2 0
%%+ procset Adobe_ColorImage_AI6 1.1 0
%%+ procset Adobe_Illustrator_AI5 1.2 0
%%+ procset Adobe_cshow 2.0 8
%AI5_FileFormat 3.0
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%AI7_ImageSettings: 0
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%%+ 1 0.5 0 0 (Bleu)
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%%+ 1 0.9 0.1 0 (Bleu fonc\216)
%%+ 0.5 0.4 0.3 0 (Bleu gris)
%%+ 0.5 0.85 1 0 (Marron)
%%+ 0.05 0.2 0.95 0 (Or)
%%+ 0 0.45 1 0 (Orange)
%%+ 0.15 1 1 0 (Rouge)
%%+ 1 0.55 1 0 (Vert)
%%+ 0.75 0.05 1 0 (Vert prairie)
%%+ 0.45 0.9 0 0 (Violet)
%%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set)
%%+ Options: 1 16 0 1 0 1 1 1 0 1 1 1 1 18 0 0 0 0 0 0 0 0 -1 -1
%%+ PPD: 1 21 0 0 60 45 2 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 ()
%AI3_TemplateBox: 306 396 306 396
%AI3_TileBox: 25 -3 585 794
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%AI5_ArtSize: 595.2756 841.8898
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%AI5_ArtFlags: 0 0 0 1 0 0 1 1 0
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%%EndComments
%%BeginProlog
%%BeginResource: procset Adobe_level2_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation)
%%Version: 1.2 0
%%CreationDate: (04/10/93) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
userdict /Adobe_level2_AI5 25 dict dup begin
	put
	/packedarray where not
	{
		userdict begin
		/packedarray
		{
			array astore readonly
		} bind def
		/setpacking /pop load def
		/currentpacking false def
	 end
		0
	} if
	pop
	userdict /defaultpacking currentpacking put true setpacking
	/initialize
	{
		Adobe_level2_AI5 begin
	} bind def
	/terminate
	{
		currentdict Adobe_level2_AI5 eq
		{
		 end
		} if
	} bind def
	mark
	/setcustomcolor where not
	{
		/findcmykcustomcolor
		{
			0
			6 packedarray
		} bind def
		/findrgbcustomcolor
		{
			1
			5 packedarray
		} bind def
		/setcustomcolor
		{
			exch
			aload pop
			0 eq
			{
				pop
				4
				{
					4 index mul
					4 1 roll
				} repeat
				5 -1 roll pop
				setcmykcolor
			}
			{
				pop
				3
				{
					1 exch sub
					3 index mul
					1 exch sub
					3 1 roll
				} repeat
				4 -1 roll pop
				setrgbcolor
			} ifelse
		}
		def
	} if

	/gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def
	userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put
	userdict /level2?
	systemdict /languagelevel known dup
	{
		pop systemdict /languagelevel get 2 ge
	} if
	put
/level2ScreenFreq
{
 begin
		60
		HalftoneType 1 eq
		{
			pop Frequency
		} if
		HalftoneType 2 eq
		{
			pop GrayFrequency
		} if
		HalftoneType 5 eq
		{
			pop Default level2ScreenFreq
		} if
 end
} bind def
userdict /currentScreenFreq
	level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put
level2? not
	{
		/setcmykcolor where not
		{
			/setcmykcolor
			{
				exch .11 mul add exch .59 mul add exch .3 mul add
				1 exch sub setgray
			} def
		} if
		/currentcmykcolor where not
		{
			/currentcmykcolor
			{
				0 0 0 1 currentgray sub
			} def
		} if
		/setoverprint where not
		{
			/setoverprint /pop load def
		} if
		/selectfont where not
		{
			/selectfont
			{
				exch findfont exch
				dup type /arraytype eq
				{
					makefont
				}
				{
					scalefont
				} ifelse
				setfont
			} bind def
		} if
		/cshow where not
		{
			/cshow
			{
				[
				0 0 5 -1 roll aload pop
				] cvx bind forall
			} bind def
		} if
	} if
	cleartomark
	/anyColor?
	{
		add add add 0 ne
	} bind def
	/testColor
	{
		gsave
		setcmykcolor currentcmykcolor
		grestore
	} bind def
	/testCMYKColorThrough
	{
		testColor anyColor?
	} bind def
	userdict /composite?
	level2?
	{
		gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore
		add add add 4 eq
	}
	{
		1 0 0 0 testCMYKColorThrough
		0 1 0 0 testCMYKColorThrough
		0 0 1 0 testCMYKColorThrough
		0 0 0 1 testCMYKColorThrough
		and and and
	} ifelse
	put
	composite? not
	{
		userdict begin
		gsave
		/cyan? 1 0 0 0 testCMYKColorThrough def
		/magenta? 0 1 0 0 testCMYKColorThrough def
		/yellow? 0 0 1 0 testCMYKColorThrough def
		/black? 0 0 0 1 testCMYKColorThrough def
		grestore
		/isCMYKSep? cyan? magenta? yellow? black? or or or def
		/customColor? isCMYKSep? not def
	 end
	} if
 end defaultpacking setpacking
%%EndResource
%%BeginProcSet: Adobe_ColorImage_AI6 1.1 0
userdict /Adobe_ColorImage_AI6 known not
{
	userdict /Adobe_ColorImage_AI6 24 dict put
} if
userdict /Adobe_ColorImage_AI6 get begin
/initialize
{
	Adobe_ColorImage_AI6 begin
	Adobe_ColorImage_AI6
	{
		dup type /arraytype eq
		{
			dup xcheck
			{
				bind
			} if
		} if
		pop pop
	} forall
} def
/terminate { end } def
currentdict /Adobe_ColorImage_AI6_Vars known not
{
	/Adobe_ColorImage_AI6_Vars 15 dict def
} if
Adobe_ColorImage_AI6_Vars begin
	/channelcount 0 def
	/sourcecount 0 def
	/sourcearray 4 array def
	/plateindex -1 def
	/XIMask 0 def
	/XIBinary 0 def
	/XIChannelCount 0 def
	/XIBitsPerPixel 0 def
	/XIImageHeight 0 def
	/XIImageWidth 0 def
	/XIImageMatrix null def
	/XIBuffer null def
	/XIDataProc null def
	/XIVersion 6 def
end
/WalkRGBString null def
/WalkCMYKString null def
/StuffRGBIntoGrayString null def
/RGBToGrayImageProc null def
/StuffCMYKIntoGrayString null def
/CMYKToGrayImageProc null def
/ColorImageCompositeEmulator null def
/SeparateCMYKImageProc null def
/FourEqual null def
/TestPlateIndex null def
currentdict /_colorimage known not
{
	/colorimage where
	{
		/colorimage get /_colorimage exch def
	}
	{
		/_colorimage null def
	} ifelse
} if
/_currenttransfer systemdict /currenttransfer get def
/colorimage null def
/XI null def
/WalkRGBString
{
	0 3 index
	dup length 1 sub 0 3 3 -1 roll
	{
		3 getinterval { } forall
		5 index exec
		3 index
	} for

	 5 { pop } repeat
} def
/WalkCMYKString
{
	0 3 index
	dup length 1 sub 0 4 3 -1 roll
	{
		4 getinterval { } forall

		6 index exec

		3 index

	} for

	5 { pop } repeat

} def
/StuffRGBIntoGrayString
{
	.11 mul exch

	.59 mul add exch

	.3 mul add

	cvi 3 copy put

	pop 1 add
} def
/RGBToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 3 idiv string
		dup 3 1 roll

		/StuffRGBIntoGrayString load exch
		WalkRGBString
 end
} def
/StuffCMYKIntoGrayString
{
	exch .11 mul add

	exch .59 mul add

	exch .3 mul add

	dup 255 gt { pop 255 } if

	255 exch sub cvi 3 copy put

	pop 1 add
} def
/CMYKToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 4 idiv string
		dup 3 1 roll

		/StuffCMYKIntoGrayString load exch
		WalkCMYKString
 end
} def
/ColorImageCompositeEmulator
{
	pop true eq
	{
		Adobe_ColorImage_AI6_Vars /sourcecount get 5 add { pop } repeat
	}
	{
		Adobe_ColorImage_AI6_Vars /channelcount get 1 ne
		{
			Adobe_ColorImage_AI6_Vars begin
				sourcearray 0 3 -1 roll put

				channelcount 3 eq
				{
					/RGBToGrayImageProc
				}
				{
					/CMYKToGrayImageProc
				} ifelse
				load
		 end
		} if
		image
	} ifelse
} def
/SeparateCMYKImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcecount 0 ne
		{
			sourcearray plateindex get exec
		}
		{
			sourcearray 0 get exec

			dup length 4 idiv string

			0 2 index

			plateindex 4 2 index length 1 sub
			{
				get 255 exch sub

				3 copy put pop 1 add

				2 index
			} for
			pop pop exch pop
		} ifelse
 end
} def

/FourEqual
{
	4 index ne
	{
		pop pop pop false
	}
	{
		4 index ne
		{
			pop pop false
		}
		{
			4 index ne
			{
				pop false
			}
			{
				4 index eq
			} ifelse
		} ifelse
	} ifelse
} def
/TestPlateIndex
{
	Adobe_ColorImage_AI6_Vars begin
		/plateindex -1 def
		/setcmykcolor where
		{
			pop
			gsave
			1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
			grestore
			1 0 0 0 FourEqual
			{
				/plateindex 0 def
			}
			{
				0 1 0 0 FourEqual
				{
					/plateindex 1 def
				}
				{
					0 0 1 0 FourEqual
					{
						/plateindex 2 def
					}
					{
						0 0 0 1 FourEqual
						{
							/plateindex 3 def
						}
						{
							0 0 0 0 FourEqual
							{
								/plateindex 5 def
							} if
						} ifelse
					} ifelse
				} ifelse
			} ifelse
			pop pop pop pop
		} if
		plateindex
 end
} def
/colorimage
{
	Adobe_ColorImage_AI6_Vars begin
		/channelcount 1 index def
		/sourcecount 2 index 1 eq { channelcount 1 sub } { 0 } ifelse def
		4 sourcecount add index dup
		8 eq exch 1 eq or not
 end

	{
		/_colorimage load null ne
		{
			_colorimage
		}
		{
			Adobe_ColorImage_AI6_Vars /sourcecount get
			7 add { pop } repeat
		} ifelse
	}
	{
		dup 3 eq
		TestPlateIndex
		dup -1 eq exch 5 eq or or
		{
			/_colorimage load null eq
			{
				ColorImageCompositeEmulator
			}
			{
				dup 1 eq
				{
					pop pop image
				}
				{
					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						gsave

						0 _currenttransfer exec
						1 _currenttransfer exec
						eq
						{ 0 _currenttransfer exec 0.5 lt }
						{ 0 _currenttransfer exec 1 _currenttransfer exec gt } ifelse

						{ { pop 0 } } { { pop 1 } } ifelse
						systemdict /settransfer get exec
					} if

					_colorimage

					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						grestore
					} if
				} ifelse
			} ifelse
		}
		{
			dup 1 eq
			{
				pop pop
				image
			}
			{
				pop pop
				Adobe_ColorImage_AI6_Vars begin
					sourcecount -1 0
					{
						exch sourcearray 3 1 roll put
					} for
					/SeparateCMYKImageProc load
			 end
				systemdict /image get exec
			} ifelse
		} ifelse
	} ifelse
} def
/XG
{
	pop pop
} def
/XF
{
	13 {pop} repeat
} def
/Xh
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIImageHeight exch def
		/XIImageWidth exch def
		/XIImageMatrix exch def
		0 0 moveto
		XIImageMatrix concat
		XIImageWidth XIImageHeight scale

		XIMask
		{
			/_lp /null ddef
			_fc
			/_lp /imagemask ddef
		}
		if
		/XIVersion 7 def
 end
} def
/XH
{
	Adobe_ColorImage_AI6_Vars begin
		/XIVersion 6 def
		grestore
 end
} def
/XI
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIBinary exch 0 ne def
		pop
		pop
		/XIChannelCount exch def
		/XIBitsPerPixel exch def
		/XIImageHeight exch def
		/XIImageWidth exch def
		pop pop pop pop
		/XIImageMatrix exch def
		XIBitsPerPixel 1 eq
		{
			XIImageWidth 8 div ceiling cvi
		}
		{
			XIImageWidth XIChannelCount mul
		} ifelse
		/XIBuffer exch string def
		XIBinary
		{
			/XIDataProc { currentfile XIBuffer readstring pop } def
			XIVersion 6 le
			{
				currentfile 128 string readline pop pop
			}
			if
		}
		{
			/XIDataProc { currentfile XIBuffer readhexstring pop } def
		} ifelse

		XIVersion 6 le
		{
			0 0 moveto
			XIImageMatrix concat
			XIImageWidth XIImageHeight scale
			XIMask
			{
				/_lp /null ddef
				_fc
				/_lp /imagemask ddef
			} if
		} if

		XIMask
		{
			XIImageWidth XIImageHeight
			false
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load
			imagemask
		}
		{
			XIImageWidth XIImageHeight
			XIBitsPerPixel
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load

			XIChannelCount 1 eq
			{
				gsave
				0 setgray
				image
				grestore
			}
			{
				false
				XIChannelCount
				colorimage
			} ifelse
		} ifelse
		grestore
 end
} def
end
%%EndProcSet
%%BeginResource: procset Adobe_Illustrator_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 7.0 Full Prolog)
%%Version: 1.2 0
%%CreationDate: (3/7/1994) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_Illustrator_AI5_vars 107 dict dup begin
put
/_eo false def
/_lp /none def
/_pf
{
} def
/_ps
{
} def
/_psf
{
} def
/_pss
{
} def
/_pjsf
{
} def
/_pjss
{
} def
/_pola 0 def
/_doClip 0 def
/cf currentflat def
/_lineorientation 0 def
/_charorientation 0 def
/_yokoorientation 0 def
/_tm matrix def
/_renderStart
[
/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0
] def
/_renderEnd
[
null null null null /i1 /i1 /i1 /i1
] def
/_render -1 def
/_shift [0 0] def
/_ax 0 def
/_ay 0 def
/_cx 0 def
/_cy 0 def
/_leading
[
0 0
] def
/_ctm matrix def
/_mtx matrix def
/_sp 16#020 def
/_hyphen (-) def
/_fontSize 0 def
/_fontAscent 0 def
/_fontDescent 0 def
/_fontHeight 0 def
/_fontRotateAdjust 0 def
/Ss 256 string def
Ss 0 (fonts/) putinterval
/_cnt 0 def
/_scale [1 1] def
/_nativeEncoding 0 def
/_useNativeEncoding 0 def
/_tempEncode 0 def
/_pntr 0 def
/_tDict 2 dict def
/_hfname 100 string def
/_hffound false def
/Tx
{
} def
/Tj
{
} def
/CRender
{
} def
/_AI3_savepage
{
} def
/_gf null def
/_cf 4 array def
/_rgbf 3 array def
/_if null def
/_of false def
/_fc
{
} def
/_gs null def
/_cs 4 array def
/_rgbs 3 array def
/_is null def
/_os false def
/_sc
{
} def
/_pd 1 dict def
/_ed 15 dict def
/_pm matrix def
/_fm null def
/_fd null def
/_fdd null def
/_sm null def
/_sd null def
/_sdd null def
/_i null def
/_lobyte 0 def
/_hibyte 0 def
/_cproc null def
/_cscript 0 def
/_hvax 0 def
/_hvay 0 def
/_hvwb 0 def
/_hvcx 0 def
/_hvcy 0 def
/_bitfont null def
/_bitlobyte 0 def
/_bithibyte 0 def
/_bitkey null def
/_bitdata null def
/_bitindex 0 def
/discardSave null def
/buffer 256 string def
/beginString null def
/endString null def
/endStringLength null def
/layerCnt 1 def
/layerCount 1 def
/perCent (%) 0 get def
/perCentSeen? false def
/newBuff null def
/newBuffButFirst null def
/newBuffLast null def
/clipForward? false def
end
userdict /Adobe_Illustrator_AI5 known not {
	userdict /Adobe_Illustrator_AI5 95 dict put
} if
userdict /Adobe_Illustrator_AI5 get begin
/initialize
{
	Adobe_Illustrator_AI5 dup begin
	Adobe_Illustrator_AI5_vars begin
	discardDict
	{
		bind pop pop
	} forall
	dup /nc get begin
	{
		dup xcheck 1 index type /operatortype ne and
		{
			bind
		} if
		pop pop
	} forall
 end
	newpath
} def
/terminate
{
 end
 end
} def
/_
null def
/ddef
{
	Adobe_Illustrator_AI5_vars 3 1 roll put
} def
/xput
{
	dup load dup length exch maxlength eq
	{
		dup dup load dup
		length 2 mul dict copy def
	} if
	load begin
	def
 end
} def
/npop
{
	{
		pop
	} repeat
} def
/hswj
{
	dup stringwidth 3 2 roll
	{
		_hvwb eq { exch _hvcx add exch _hvcy add } if
		exch _hvax add exch _hvay add
	} cforall
} def
/vswj
{
	0 0 3 -1 roll
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			dup cstring stringwidth 5 2 roll
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			4 -1 roll sub exch
			3 -1 roll sub exch
		}
		{
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			_fontHeight sub
		} ifelse
	} cforall
} def
/swj
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hswj } { vswj } ifelse
} def
/sw
{
	0 0 0 6 3 roll swj
} def
/vjss
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			gsave
			false charpath currentpoint
			5 index setmatrix stroke
			grestore
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			gsave
			2 index false charpath
			6 index setmatrix stroke
			grestore

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjss
{
	4 1 roll
	{
		dup cstring
		gsave
		false charpath currentpoint
		5 index setmatrix stroke
		grestore
		moveto
		_sp eq
		{
			5 index 5 index rmoveto
		} if
		2 copy rmoveto
	} cforall
	6 npop
} def
/jss
{
	_lineorientation 0 eq { hjss } { vjss } ifelse
} def
/ss
{
	0 0 0 7 3 roll jss
} def
/vjsp
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			false charpath
            currentpoint
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			2 index false charpath

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjsp
{
    4 1 roll
    {
        dup cstring
        false charpath
        _sp eq
        {
            5 index 5 index rmoveto
        } if
        2 copy rmoveto
    } cforall
    6 npop
} def
/jsp
{
	matrix currentmatrix
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/sp
{
    matrix currentmatrix
    0 0 0 7 3 roll
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/pl
{
	transform
	0.25 sub round 0.25 add exch
	0.25 sub round 0.25 add exch
	itransform
} def
/setstrokeadjust where
{
	pop true setstrokeadjust
	/c
	{
		curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll curveto
	} def
	/V
	/v load def
	/y
	{
		2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		lineto
	} def
	/L
	/l load def
	/m
	{
		moveto
	} def
}
{
	/c
	{
		pl curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll pl curveto
	} def
	/V
	/v load def
	/y
	{
		pl 2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		pl lineto
	} def
	/L
	/l load def
	/m
	{
		pl moveto
	} def
} ifelse
/d
{
	setdash
} def
/cf
{
} def
/i
{
	dup 0 eq
	{
		pop cf
	} if
	setflat
} def
/j
{
	setlinejoin
} def
/J
{
	setlinecap
} def
/M
{
	setmiterlimit
} def
/w
{
	setlinewidth
} def
/XR
{
	0 ne
	/_eo exch ddef
} def
/H
{
} def
/h
{
	closepath
} def
/N
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			_eo {eoclip} {clip} ifelse /_doClip 0 ddef
		} if
		newpath
	}
	{
		/CRender
		{
			N
		} ddef
	} ifelse
} def
/n
{
	N
} def
/F
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc
			/_doClip 0 ddef
		}
		{
			_pf
		} ifelse
	}
	{
		/CRender
		{
			F
		} ddef
	} ifelse
} def
/f
{
	closepath
	F
} def
/S
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			_ps
		} ifelse
	}
	{
		/CRender
		{
			S
		} ddef
	} ifelse
} def
/s
{
	closepath
	S
} def
/B
{
	_pola 0 eq
	{
		_doClip 1 eq
		gsave F grestore
		{
			gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			S
		} ifelse
	}
	{
		/CRender
		{
			B
		} ddef
	} ifelse
} def
/b
{
	closepath
	B
} def
/W
{
	/_doClip 1 ddef
} def
/*
{
	count 0 ne
	{
		dup type /stringtype eq
		{
			pop
		} if
	} if
	newpath
} def
/u
{
} def
/U
{
} def
/q
{
	_pola 0 eq
	{
		gsave
	} if
} def
/Q
{
	_pola 0 eq
	{
		grestore
	} if
} def
/*u
{
	_pola 1 add /_pola exch ddef
} def
/*U
{
	_pola 1 sub /_pola exch ddef
	_pola 0 eq
	{
		CRender
	} if
} def
/D
{
	pop
} def
/*w
{
} def
/*W
{
} def
/`
{
	/_i save ddef
	clipForward?
	{
		nulldevice
	} if
	6 1 roll 4 npop
	concat pop
	userdict begin
	/showpage
	{
	} def
	0 setgray
	0 setlinecap
	1 setlinewidth
	0 setlinejoin
	10 setmiterlimit
	[] 0 setdash
	/setstrokeadjust where {pop false setstrokeadjust} if
	newpath
	0 setgray
	false setoverprint
} def
/~
{
 end
	_i restore
} def
/O
{
	0 ne
	/_of exch ddef
	/_lp /none ddef
} def
/R
{
	0 ne
	/_os exch ddef
	/_lp /none ddef
} def
/g
{
	/_gf exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_gf setgray
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/G
{
	/_gs exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_gs setgray
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/k
{
	_cf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_cf aload pop setcmykcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/K
{
	_cs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_cs aload pop setcmykcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/Xa
{
	_rgbf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_rgbf aload pop setrgbcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XA
{
	_rgbs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_rgbs aload pop setrgbcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/_rgbtocmyk
{
3
	{
	1 exch sub 3 1 roll
	} repeat
3 copy 1 4 1 roll
3
	{
	3 index 2 copy gt
		{
		exch
		} if
	pop 4 1 roll
	} repeat
pop pop pop
4 1 roll
3
	{
	3 index sub
	3 1 roll
	} repeat
4 -1 roll
} def
/Xx
{
	exch
	/_gf exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XX
{
	exch
	/_gs exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/x
{
	/_gf exch ddef
	findcmykcustomcolor
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/X
{
	/_gs exch ddef
	findcmykcustomcolor
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/A
{
	pop
} def
/annotatepage
{
userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse
} def
/XT {
	pop pop
} def
/discard
{
	save /discardSave exch store
	discardDict begin
	/endString exch store
	gt38?
	{
		2 add
	} if
	load
	stopped
	pop
 end
	discardSave restore
} bind def
userdict /discardDict 7 dict dup begin
put
/pre38Initialize
{
	/endStringLength endString length store
	/newBuff buffer 0 endStringLength getinterval store
	/newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store
	/newBuffLast newBuff endStringLength 1 sub 1 getinterval store
} def
/shiftBuffer
{
	newBuff 0 newBuffButFirst putinterval
	newBuffLast 0
	currentfile read not
	{
	stop
	} if
	put
} def
0
{
	pre38Initialize
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff endString eq
			{
				cleartomark stop
			} if
			shiftBuffer
		} loop
	}
	{
	stop
	} ifelse
} def
1
{
	pre38Initialize
	/beginString exch store
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff beginString eq
			{
				/layerCount dup load 1 add store
			}
			{
				newBuff endString eq
				{
					/layerCount dup load 1 sub store
					layerCount 0 eq
					{
						cleartomark stop
					} if
				} if
			} ifelse
			shiftBuffer
		} loop
	} if
} def
2
{
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		endString eq
		{
			cleartomark stop
		} if
	} loop
} def
3
{
	/beginString exch store
	/layerCnt 1 store
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		dup beginString eq
		{
			pop /layerCnt dup load 1 add store
		}
		{
			endString eq
			{
				layerCnt 1 eq
				{
					cleartomark stop
				}
				{
					/layerCnt dup load 1 sub store
				} ifelse
			} if
		} ifelse
	} loop
} def
end
userdict /clipRenderOff 15 dict dup begin
put
{
	/n /N /s /S /f /F /b /B
}
{
	{
		_doClip 1 eq
		{
			/_doClip 0 ddef _eo {eoclip} {clip} ifelse
		} if
		newpath
	} def
} forall
/Tr /pop load def
/Bb {} def
/BB /pop load def
/Bg {12 npop} def
/Bm {6 npop} def
/Bc /Bm load def
/Bh {4 npop} def
end
/Lb
{
	4 npop
	6 1 roll
	pop
	4 1 roll
	pop pop pop
	0 eq
	{
		0 eq
		{
			(%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard
		}
		{

			/clipForward? true def

			/Tx /pop load def
			/Tj /pop load def

			currentdict end clipRenderOff begin begin
		} ifelse
	}
	{
		0 eq
		{
			save /discardSave exch store
		} if
	} ifelse
} bind def
/LB
{
	discardSave dup null ne
	{
		restore
	}
	{
		pop
		clipForward?
		{
			currentdict
		 end
		 end
		 begin

			/clipForward? false ddef
		} if
	} ifelse
} bind def
/Pb
{
	pop pop
	0 (%AI5_EndPalette) discard
} bind def
/Np
{
	0 (%AI5_End_NonPrinting--) discard
} bind def
/Ln /pop load def
/Ap
/pop load def
/Ar
{
	72 exch div
	0 dtransform dup mul exch dup mul add sqrt
	dup 1 lt
	{
		pop 1
	} if
	setflat
} def
/Mb
{
	q
} def
/Md
{
} def
/MB
{
	Q
} def
/nc 4 dict def
nc begin
/setgray
{
	pop
} bind def
/setcmykcolor
{
	4 npop
} bind def
/setrgbcolor
{
	3 npop
} bind def
/setcustomcolor
{
	2 npop
} bind def
currentdict readonly pop
end
end
setpacking
%%EndResource
%%BeginResource: procset Adobe_cshow 2.0 8
%%Title: (Writing System Operators)
%%Version: 2.0 8
%%CreationDate: (1/23/89) ()
%%Copyright: ((C) 1992-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_cshow 14 dict dup begin put
/initialize
{
	Adobe_cshow begin
	Adobe_cshow
	{
		dup xcheck
		{
			bind
		} if
		pop pop
	} forall
 end
	Adobe_cshow begin
} def
/terminate
{
currentdict Adobe_cshow eq
	{
 end
	} if
} def
/cforall
{
	/_lobyte 0 ddef
	/_hibyte 0 ddef
	/_cproc exch ddef
	/_cscript currentfont /FontScript known { currentfont /FontScript get } { -1 } ifelse ddef
	{
		/_lobyte exch ddef
		_hibyte 0 eq
		_cscript 1 eq
		_lobyte 129 ge _lobyte 159 le and
		_lobyte 224 ge _lobyte 252 le and or and
		_cscript 2 eq
		_lobyte 161 ge _lobyte 254 le and and
		_cscript 3 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript 25 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript -1 eq
		or or or or and
		{
			/_hibyte _lobyte ddef
		}
		{
			_hibyte 256 mul _lobyte add
			_cproc
			/_hibyte 0 ddef
		} ifelse
	} forall
} def
/cstring
{
	dup 256 lt
	{
		(s) dup 0 4 3 roll put
	}
	{
		dup 256 idiv exch 256 mod
		(hl) dup dup 0 6 5 roll put 1 4 3 roll put
	} ifelse
} def
/clength
{
	0 exch
	{ 256 lt { 1 } { 2 } ifelse add } cforall
} def
/hawidthshow
{
	{
		dup cstring
		show
		_hvax _hvay rmoveto
		_hvwb eq { _hvcx _hvcy rmoveto } if
	} cforall
} def
/vawidthshow
{
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			-90 rotate
			0 _fontRotateAdjust rmoveto
			cstring
			_hvcx _hvcy _hvwb _hvax _hvay 6 -1 roll awidthshow
			0 _fontRotateAdjust neg rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			exch _hvay sub exch _hvax sub
			2 index _hvwb eq { exch _hvcy sub exch _hvcx sub } if
			3 2 roll
			cstring
			dup stringwidth pop 2 div neg _fontAscent neg rmoveto
			show
			moveto
		} ifelse
	} cforall
} def
/hvawidthshow
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hawidthshow } { vawidthshow } ifelse
} def
/hvwidthshow
{
	0 0 3 -1 roll hvawidthshow
} def
/hvashow
{
	0 0 0 6 -3 roll hvawidthshow
} def
/hvshow
{
	0 0 0 0 0 6 -1 roll hvawidthshow
} def
currentdict readonly pop end
setpacking
%%EndResource
%%EndProlog
%%BeginSetup
Adobe_level2_AI5 /initialize get exec
Adobe_cshow /initialize get exec
Adobe_ColorImage_AI6 /initialize get exec
Adobe_Illustrator_AI5 /initialize get exec
%AI5_Begin_NonPrinting
Np
%AI3_BeginPattern: (Acailles)
(Acailles) 1.6 9.3475 48.088 55.8355 [
%AI3_Tile
(0 O 0 R  1 g
 1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 9.3475 m
1.6 55.8355 L
48.088 55.8355 L
48.088 9.3475 L
1.6 9.3475 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R  0 g
 0 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
17.0956 9.3475 m
12.8162 9.3475 9.3475 5.8787 9.3475 1.6 C
9.3475 5.8787 5.8787 9.3475 1.6 9.3475 C
1.6 13.6262 5.0687 17.095 9.3475 17.095 c
13.6268 17.095 17.0956 13.6262 17.0956 9.3475 C
s
32.5918 9.3475 m
28.3125 9.3475 24.8437 5.8787 24.8437 1.6 C
24.8437 5.8787 21.3743 9.3475 17.0956 9.3475 C
17.0956 13.6262 20.5644 17.095 24.8437 17.095 c
29.1224 17.095 32.5918 13.6262 32.5918 9.3475 C
s
48.088 9.3475 m
43.8087 9.3475 40.3399 5.8787 40.3399 1.6 C
40.3399 5.8787 36.8705 9.3475 32.5918 9.3475 C
32.5918 13.6262 36.0606 17.095 40.3399 17.095 c
44.6186 17.095 48.088 13.6262 48.088 9.3475 C
s
17.0956 40.3393 m
12.8162 40.3393 9.3475 36.8699 9.3475 32.5912 C
9.3475 36.8699 5.8787 40.3393 1.6 40.3393 C
1.6 44.6181 5.0687 48.0874 9.3475 48.0874 c
13.6268 48.0874 17.0956 44.6181 17.0956 40.3393 C
s
17.0956 24.8431 m
12.8162 24.8431 9.3475 21.3743 9.3475 17.095 C
9.3475 21.3743 5.8787 24.8431 1.6 24.8431 C
1.6 29.1218 5.0687 32.5912 9.3475 32.5912 c
13.6268 32.5912 17.0956 29.1218 17.0956 24.8431 C
s
32.5918 24.8431 m
28.3125 24.8431 24.8437 21.3743 24.8437 17.095 C
24.8437 21.3743 21.3743 24.8431 17.0956 24.8431 C
17.0956 29.1218 20.5644 32.5912 24.8437 32.5912 c
29.1224 32.5912 32.5918 29.1218 32.5918 24.8431 C
s
48.088 24.8431 m
43.8087 24.8431 40.3399 21.3743 40.3399 17.095 C
40.3399 21.3743 36.8705 24.8431 32.5918 24.8431 C
32.5918 29.1218 36.0606 32.5912 40.3399 32.5912 c
44.6186 32.5912 48.088 29.1218 48.088 24.8431 C
s
32.5918 40.3393 m
28.3125 40.3393 24.8437 36.8699 24.8437 32.5912 C
24.8437 36.8699 21.3743 40.3393 17.0956 40.3393 C
17.0956 44.6181 20.5644 48.0874 24.8437 48.0874 c
29.1224 48.0874 32.5918 44.6181 32.5918 40.3393 C
s
48.088 40.3393 m
43.8087 40.3393 40.3399 36.8699 40.3399 32.5912 C
40.3399 36.8699 36.8705 40.3393 32.5918 40.3393 C
32.5918 44.6181 36.0606 48.0874 40.3399 48.0874 c
44.6186 48.0874 48.088 44.6181 48.088 40.3393 C
s
17.0956 55.8355 m
12.8162 55.8355 9.3475 52.3662 9.3475 48.0874 C
9.3475 52.3662 5.8787 55.8355 1.6 55.8355 C
1.6 60.1143 5.0687 63.5836 9.3475 63.5836 c
13.6268 63.5836 17.0956 60.1143 17.0956 55.8355 C
s
32.5918 55.8355 m
28.3125 55.8355 24.8437 52.3662 24.8437 48.0874 C
24.8437 52.3662 21.3743 55.8355 17.0956 55.8355 C
17.0956 60.1143 20.5644 63.5836 24.8437 63.5836 c
29.1224 63.5836 32.5918 60.1143 32.5918 55.8355 C
s
48.088 55.8355 m
43.8087 55.8355 40.3399 52.3662 40.3399 48.0874 C
40.3399 52.3662 36.8705 55.8355 32.5918 55.8355 C
32.5918 60.1143 36.0606 63.5836 40.3399 63.5836 c
44.6186 63.5836 48.088 60.1143 48.088 55.8355 C
s
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Bandes transparentes)
(Bandes transparentes) 8.45 4.6001 80.45 76.6001 [
%AI3_Tile
(0 O 0 R  1 0.07 1 0 k
 1 0.07 1 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 3.6 w 4 M []0 d
%AI3_Note:
0 D
0 XR
8.2 8.2 m
80.7 8.2 L
S
8.2 22.6001 m
80.7 22.6001 L
S
8.2 37.0002 m
80.7 37.0002 L
S
8.2 51.4 m
80.7 51.4 L
S
8.2 65.8001 m
80.7 65.8001 L
S
8.2 15.4 m
80.7 15.4 L
S
8.2 29.8001 m
80.7 29.8001 L
S
8.2 44.2 m
80.7 44.2 L
S
8.2 58.6001 m
80.7 58.6001 L
S
8.2 73.0002 m
80.7 73.0002 L
S
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Briques)
(Briques) 1.6 1.6 73.6 73.6 [
%AI3_Tile
(0 O 0 R  0.3 0.85 0.85 0 k
 0.3 0.85 0.85 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 1.6 m
1.6 73.6 L
73.6 73.6 L
73.6 1.6 L
1.6 1.6 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R  1 g
 1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 70.01 m
73.6 70.01 l
S
1.6 62.809 m
73.6 62.809 L
S
1.6 55.609 m
73.6 55.609 L
S
1.6 48.408 m
73.6 48.408 L
S
1.6 41.208 m
73.6 41.208 L
S
1.6 34.007 m
73.6 34.007 L
S
1.6 26.807 m
73.6 26.807 L
S
1.6 19.606 m
73.6 19.606 L
S
1.6 12.406 m
73.6 12.406 L
S
1.6 5.206 m
73.6 5.206 L
S
70.01 70.01 m
70.01 62.822 l
S
55.61 70.01 m
55.61 62.822 L
S
41.21 70.01 m
41.21 62.822 L
S
26.81 70.01 m
26.81 62.822 L
S
12.41 70.01 m
12.41 62.822 L
S
70.01 55.572 m
70.01 48.385 l
S
55.61 55.572 m
55.61 48.385 L
S
41.21 55.572 m
41.21 48.385 L
S
26.81 55.572 m
26.81 48.385 L
S
12.41 55.572 m
12.41 48.385 L
S
70.01 41.197 m
70.01 34.01 l
S
55.61 41.197 m
55.61 34.01 L
S
41.21 41.197 m
41.21 34.01 L
S
26.81 41.197 m
26.81 34.01 L
S
12.41 41.197 m
12.41 34.01 L
S
70.01 26.822 m
70.01 19.635 l
S
55.61 26.822 m
55.61 19.635 L
S
41.21 26.822 m
41.21 19.635 L
S
26.81 26.822 m
26.81 19.635 L
S
12.41 26.822 m
12.41 19.635 L
S
70.01 12.385 m
70.01 5.197 l
S
55.61 12.385 m
55.61 5.197 L
S
41.21 12.385 m
41.21 5.197 L
S
26.81 12.385 m
26.81 5.197 L
S
12.41 12.385 m
12.41 5.197 L
S
62.797 5.197 m
62.797 1.6 L
S
48.397 5.197 m
48.397 1.6 L
S
33.997 5.197 m
33.997 1.6 L
S
19.597 5.197 m
19.597 1.6 L
S
5.197 5.197 m
5.197 1.6 l
S
62.797 19.635 m
62.797 12.447 L
S
48.397 19.635 m
48.397 12.447 L
S
33.997 19.635 m
33.997 12.447 L
S
19.597 19.635 m
19.597 12.447 L
S
5.197 19.635 m
5.197 12.447 l
S
62.797 34.01 m
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551.1486 690.477 549.2568 692.3688 546.9232 692.3688 c
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542.6977 685.8097 544.5895 683.9178 546.9232 683.9178 c
f
508.7449 683.9178 m
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512.9703 690.477 511.0785 692.3688 508.7449 692.3688 c
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f
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f
508.7449 609.5531 m
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f
546.9232 647.0674 m
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f
508.7449 647.0674 m
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512.9703 653.6266 511.0785 655.5184 508.7449 655.5184 c
506.4112 655.5184 504.5193 653.6266 504.5193 651.2929 c
504.5193 648.9593 506.4112 647.0674 508.7449 647.0674 c
f
358.6874 647.0674 m
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f
358.6874 609.5531 m
361.0211 609.5531 362.9129 611.4449 362.9129 613.7786 c
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f
434.0482 647.0674 m
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f
434.0482 609.5531 m
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f
358.6874 570.9525 m
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356.3538 579.4034 354.4619 577.5116 354.4619 575.178 c
354.4619 572.8443 356.3538 570.9525 358.6874 570.9525 c
f
321.837 570.6205 m
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f
508.7449 721.7642 m
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f
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f
396.5338 683.9178 m
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f
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f
358.6874 683.9178 m
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f
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f
470.8985 721.7642 m
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f
470.8985 759.9425 m
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f
434.3801 721.7642 m
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f
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f
434.3801 571.3748 m
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f
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f
434.3801 759.9425 m
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432.0465 768.3935 430.1546 766.5017 430.1546 764.168 c
430.1546 761.8344 432.0465 759.9425 434.3801 759.9425 c
f
0 Ap
0 0 1 Xa
0 R
0 0 0 XA
4 w
358.6874 613.6126 m
358.6874 650.463 l
B
471.4868 763.836 m
508.3372 763.836 l
B
1 Ap
1 g
0 0 0 1 K
208.9232 727.5768 m
208.9232 765.4232 L
171.0768 765.4232 L
171.0768 727.5768 L
208.9232 727.5768 L
b
LB
%AI5_EndLayer--
%%PageTrailer
gsave annotatepage grestore showpage
%%Trailer
Adobe_Illustrator_AI5 /terminate get exec
Adobe_ColorImage_AI6 /terminate get exec
Adobe_cshow /terminate get exec
Adobe_level2_AI5 /terminate get exec
%%EOF

%%EndDocument
 @endspecial 7188 56054 a(Figure)433 b(1:)579 b(A)433
b(set)h(of)g(b)36 b(onds)433 b Fu(X)539 b Fx(and)433
b(its)g(asso)36 b(ciated)435 b(cell)f(complex)g(\244\()p
Fu(X)104 b Fx(\).)6268 59432 y(F)-108 b(or)531 b(a)g(set)g(of)g(b)36
b(onds)531 b Fu(X)104 b Fx(,)556 b(w)-36 b(e)531 b(de\257ne)f(the)h(b)
36 b(oundary)530 b Fu(B)67 b Fx(\()p Fu(X)104 b Fx(\)of)532
b Fu(X)636 b Fx(as)532 b(the)e(set)h(of)4317 61037 y(b)36
b(onds)476 b(of)g Fu(X)581 b Fx(that)476 b(b)36 b(elong)477
b(to)f(a)g(plaquette)g(of)h Fu(L)29357 61236 y Fs(2)30207
61037 y Fr(n)324 b Fx(\244)32098 61236 y Fs(2)32624 61037
y Fx(\()p Fu(X)104 b Fx(\).)707 b(W)-108 b(e)476 b(also)h(asso)36
b(ciate)477 b(to)4317 62642 y(the)433 b(set)h(of)g(b)36
b(onds)433 b Fu(X)538 b Fx(the)433 b(o)36 b(ccupation)434
b(n)-36 b(um)g(b)36 b(er)19658 66086 y Fu(n)20434 66285
y Fq(b)21261 66086 y Fx(=)22642 64213 y Fj(\275)24192
65272 y Fx(1)1107 b(if)1394 b Fu(b)369 b Fr(2)f Fu(X)24192
66877 y Fx(0)1107 b(otherwise)45827 66086 y(\(1\))25578
70015 y(4)p eop
%%Page: 5 5
5 4 bop 4317 7306 a Fx(and)651 b(denote)f(b)-36 b(y)651
b Fu(n)740 b Fr(\264)g(f)p Fu(n)18225 7505 y Fq(b)18683
7306 y Fr(g)19347 7693 y Fq(b)p Fp(2)p Fi(L)20967 7816
y Fo(1)22135 7306 y Fx(the)651 b(asso)36 b(ciated)652
b(con\257guration.)1231 b(W)-108 b(e)651 b(then)f(use)4317
8911 y Fu(N)5498 8429 y Fs(0)6023 8911 y Fx(\()p Fu(n)p
Fx(\))416 b Fr(\264)g(j)p Fx(\244)10948 9110 y Fs(0)11474
8911 y Fx(\()p Fu(X)104 b Fx(\))p Fr(j)462 b Fx(to)f(denote)f(the)h(n)
-36 b(um)g(b)36 b(er)460 b(of)i(sites)f(of)h(\244)34217
9110 y Fs(0)34742 8911 y Fx(\()p Fu(X)104 b Fx(\),)469
b Fu(N)38948 8429 y Fs(1)39473 8911 y Fx(\()p Fu(n)p
Fx(\))416 b Fr(\264)g(j)p Fx(\244)44398 9110 y Fs(1)44924
8911 y Fx(\()p Fu(X)104 b Fx(\))p Fr(j)4317 10516 y Fx(to)522
b(denote)g(the)g(n)-36 b(um)g(b)36 b(er)520 b(of)j(b)36
b(onds)522 b(of)g(\244)25357 10715 y Fs(1)25883 10516
y Fx(\()p Fu(X)104 b Fx(\),)545 b(and)522 b Fu(N)32783
10034 y Fs(2)33308 10516 y Fx(\()p Fu(n)p Fx(\))e Fr(\264)g(j)p
Fx(\244)38441 10715 y Fs(2)38966 10516 y Fx(\()p Fu(X)104
b Fx(\))p Fr(j)523 b Fx(to)f(denote)4317 12121 y(the)452
b(n)-36 b(um)g(b)36 b(er)452 b(of)h(plaquettes)g(of)h(\244)21510
12320 y Fs(2)22035 12121 y Fx(\()p Fu(X)104 b Fx(\).)637
b(Hereafter)453 b(w)-36 b(e)453 b(will)h(use)e Fr(j)p
Fu(E)78 b Fr(j)453 b Fx(to)g(denote)f(the)4317 13726
y(cardinalit)-36 b(y)434 b(of)h(the)e(set)g Fu(E)78 b
Fx(.)6268 15819 y(The)434 b(Euler)f(c)-36 b(haracteristic)434
b(of)g(\244\()p Fu(X)104 b Fx(\))434 b(is)g(de\257ned)e(b)-36
b(y)16829 17981 y Fu(\302)-786 b(\302)g(\302)g(\302)p
Fx(\()p Fu(n)p Fx(\))369 b(=)f Fu(N)22449 17433 y Fs(0)22975
17981 y Fx(\()p Fu(n)p Fx(\))295 b Fr(\241)g Fu(N)27567
17433 y Fs(1)28092 17981 y Fx(\()p Fu(n)p Fx(\))g(+)g
Fu(N)32663 17433 y Fs(2)33188 17981 y Fx(\()p Fu(n)p
Fx(\))10851 b(\(2\))4317 20144 y(It)434 b(satis\257es)g(the)f(Euler{P)
-36 b(oincar)g(\266)-614 b(e)433 b(form)-36 b(ula)17422
22306 y Fu(\302)-786 b(\302)g(\302)g(\302)o Fx(\()p Fu(n)p
Fx(\))369 b(=)g Fu(\274)22647 21758 y Fs(0)23172 22306
y Fx(\()p Fu(n)p Fx(\))295 b Fr(\241)h Fu(\274)27370
21758 y Fs(1)27895 22306 y Fx(\()p Fu(n)p Fx(\))f(+)g
Fu(\274)32071 21758 y Fs(2)32596 22306 y Fx(\()p Fu(n)p
Fx(\))11443 b(\(3\))4317 24469 y(where)365 b Fu(\274)8792
23986 y Fs(0)9317 24469 y Fx(\()p Fu(n)p Fx(\))g(and)f
Fu(\274)14716 23986 y Fs(1)15241 24469 y Fx(\()p Fu(n)p
Fx(\))h(are)g(resp)36 b(ectiv)-36 b(ely)366 b(the)e(n)-36
b(um)g(b)36 b(er)363 b(of)i(connected)f(comp)36 b(onen)-36
b(ts)4317 26074 y(and)473 b(the)f(maximal)i(n)-36 b(um)g(b)36
b(er)471 b(of)j(indep)36 b(enden)-36 b(t)471 b(1-cycles)j(of)f(\244\()p
Fu(X)104 b Fx(\).)697 b(Here)473 b Fu(\274)42642 25592
y Fs(2)43167 26074 y Fx(\()p Fu(n)p Fx(\))436 b(=)f(0)4317
27679 y(b)36 b(ecause)434 b(\244\()p Fu(X)104 b Fx(\))433
b(has)h(no)f(2-cycles.)6268 29771 y(Our)301 b(aim)h(is)h(to)f(study)f
(the)g(mean)h(v)-72 b(alue)302 b(of)h(the)e(Euler)h(c)-36
b(haracteristic)302 b(with)g(resp)36 b(ect)4317 31376
y(to)432 b(the)g(F)-108 b(ortuin{Kasteleyn)432 b(measure.)578
b(T)-108 b(o)432 b(in)-36 b(tro)36 b(duce)431 b(this)h(measure)g(w)-36
b(e)432 b(de\257ne,)g(for)4317 32982 y(a)i(\\v)-36 b(olume")435
b Fu(V)658 b Fr(\275)369 b Ft(L)14886 33181 y Fs(1)15412
32982 y Fx(,)433 b(the)g(partition)h(functions)f(with)h(b)36
b(oundary)433 b(conditions)9193 35303 y Fu(Z)10178 34754
y Fs(b)26 b(c)11201 35303 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))370 b(=)18458 34041 y Fj(X)17391
37099 y Fq(n)p Fp(2f)p Fs(0)p Fq(;)p Fs(1)p Fp(g)20732
36708 y Fn(V)21444 35303 y Fx(\()p Fu(e)22553 34754 y
Fq(\257)23477 35303 y Fr(\241)295 b Fx(1\))25961 34754
y Fq(N)26802 34442 y Fo(1)27264 34754 y Fs(\()p Fq(n)p
Fs(\))28622 35303 y Fu(q)29247 34754 y Fp(j)p Fs(\244)30161
34877 y Fo(0)30621 34754 y Fs(\()p Fq(V)209 b Fs(\))p
Fp(j)q(\241)p Fq(N)33945 34442 y Fo(0)34406 34754 y Fs(\()p
Fq(n)p Fs(\)+)p Fq(\274)37013 34442 y Fo(0)37474 34754
y Fs(\()p Fq(n)p Fs(\))39053 35303 y Fu(\267)39802 34754
y Fs(b)26 b(c)40824 35303 y Fx(\()p Fu(n)p Fx(\))3215
b(\(4\))4317 39044 y(and)439 b(the)f(corresp)36 b(onding)439
b(\257nite)f(v)-36 b(olume)439 b(exp)36 b(ectations)440
b(of)f(lo)36 b(cal)441 b(functions)e Fu(f)580 b Fx(of)440
b(the)4317 40649 y(b)36 b(onds)433 b(v)-72 b(ariable)434
b Fr(f)p Fu(n)14435 40848 y Fq(b)14894 40649 y Fr(g)g
Fx(b)-36 b(y)4887 43403 y Fr(h)p Fu(f)142 b Fr(i)6704
42855 y Fs(b)26 b(c)7726 43403 y Fx(\()p Fu(V)72 b(;)221
b(\257)74 b(;)221 b(q)48 b Fx(\))369 b(=)16868 42505
y(1)p 14048 43098 6291 54 v 14048 44315 a Fu(Z)15033
43931 y Fq(bc)15899 44315 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))21760 42142 y Fj(X)20693 45200
y Fq(n)p Fp(2f)p Fs(0)p Fq(;)p Fs(1)p Fp(g)24034 44809
y Fn(V)24968 43403 y Fu(f)142 b Fx(\()p Fu(e)26860 42855
y Fq(\257)27783 43403 y Fr(\241)296 b Fx(1\))30268 42855
y Fq(N)31109 42543 y Fo(1)31570 42855 y Fs(\()p Fq(n)p
Fs(\))32928 43403 y Fu(q)33553 42855 y Fp(j)p Fs(\244)34467
42978 y Fo(0)34928 42855 y Fs(\()p Fq(V)209 b Fs(\))p
Fp(j\241)p Fq(N)38251 42543 y Fo(0)38712 42855 y Fs(\()p
Fq(n)p Fs(\)+)p Fq(\274)41319 42543 y Fo(0)41780 42855
y Fs(\()p Fq(n)p Fs(\))43360 43403 y Fu(\267)44109 42855
y Fs(b)26 b(c)45131 43403 y Fx(\()p Fu(n)p Fx(\))45827
46661 y(\(5\))4317 48266 y(where)472 b Fu(\267)8862 47784
y Fs(b)26 b(c)9884 48266 y Fx(\()p Fu(n)p Fx(\))472 b(refers)h(to)f
(the)g(b)36 b(oundary)471 b(condition)h(b)36 b(c.)694
b(In)472 b(particular,)482 b(w)-36 b(e)472 b(will)i(b)36
b(e)4317 49871 y(in)-36 b(terested)525 b(to)g(the)g(free)h(b)36
b(oundary)525 b(condition)g Fu(\267)29470 49389 y Fs(f)29883
49871 y Fx(\()p Fu(n)p Fx(\))g(=)g(1)h(and)f(to)h(the)f(ordered)f(or)
4317 51476 y(wired)434 b(b)36 b(oundary)433 b(condition)g
Fu(\267)20168 50994 y Fs(w)20916 51476 y Fx(\()p Fu(n)p
Fx(\))369 b(=)24454 50480 y Fj(Q)25708 51864 y Fq(b)p
Fp(2)p Fq(B)44 b Fs(\()p Fq(V)208 b Fs(\))29257 51476
y Fu(n)30033 51675 y Fq(b)30491 51476 y Fx(.)6268 53993
y(Notice)434 b(that)f(for)i(a)e(con\257guration)h Fu(n)369
b Fr(2)g(f)p Fx(0)p Fu(;)221 b Fx(1)p Fr(g)29727 53348
y Fp(j)q Fq(V)209 b Fp(j)31062 53993 y Fx(,)434 b(one)g(has)14778
56388 y Fu(N)15959 55840 y Fs(0)16485 56388 y Fx(\()p
Fu(n)p Fx(\))369 b(=)f(\244)20925 56587 y Fs(0)21451
56388 y Fx(\()p Fu(V)289 b Fx(\))295 b Fr(\241)26054
55126 y Fj(X)25133 58004 y Fq(x)p Fp(2)p Fs(\244)26943
58127 y Fo(0)27404 58004 y Fs(\()p Fq(V)209 b Fs(\))29962
55126 y Fj(Y)29114 57955 y Fq(b)p Fp(2)p Fq(\261)33 b(x)p
Fp(\\)p Fq(V)32508 56388 y Fx(\(1)295 b Fr(\241)g Fu(n)36063
56587 y Fq(b)36521 56388 y Fx(\))14778 60556 y Fu(N)15959
60008 y Fs(1)16485 60556 y Fx(\()p Fu(n)p Fx(\))369 b(=)20943
59294 y Fj(X)20022 62172 y Fq(x)p Fp(2)p Fs(\244)21832
62295 y Fo(0)22293 62172 y Fs(\()p Fq(V)209 b Fs(\))24136
59657 y Fx(1)p 24136 60251 651 54 v 24136 61467 a(2)25878
59294 y Fj(X)25141 62123 y Fq(b)p Fp(2)p Fq(\261)33 b(x)p
Fp(\\)p Fq(V)28755 60556 y Fu(n)29531 60755 y Fq(b)14778
64724 y Fu(N)15959 64175 y Fs(2)16485 64724 y Fx(\()p
Fu(n)p Fx(\))369 b(=)20943 63462 y Fj(X)20022 66340 y
Fq(x)p Fp(2)p Fs(\244)21832 66463 y Fo(0)22293 66340
y Fs(\()p Fq(V)209 b Fs(\))24136 63825 y Fx(1)p 24136
64418 V 24136 65635 a(4)25726 63462 y Fj(X)25141 66340
y Fq(p)p Fp(2)p Fq(P)131 b Fs(\()p Fq(x)p Fs(\))29321
63462 y Fj(Y)28452 66291 y Fq(b)p Fp(2)p Fq(@)52 b(p)p
Fp(\\)p Fq(V)32109 64724 y Fu(n)32885 64923 y Fq(b)25578
70015 y Fx(5)p eop
%%Page: 6 6
6 5 bop 4317 7306 a Fx(where)440 b Fu(P)181 b Fx(\()p
Fu(x)p Fx(\))439 b(is)i(the)e(set)g(of)i(the)e(four)h(plaquettes)g
(that)f(in)-36 b(tersect)440 b Fu(x)p Fx(.)597 b(This)440
b(represen-)4317 8911 y(tation)434 b(motiv)-72 b(ates)434
b(the)f(follo)-36 b(wing)436 b(de\257nition)d(of)h(the)f(lo)36
b(cal)435 b(Euler)e(c)-36 b(haracteristic.)11131 12309
y Fu(\302)11946 12508 y Fq(x)12530 12309 y Fx(\()p Fu(n)p
Fx(\))369 b Fr(\264)h Fx(1)295 b Fr(\241)18519 11047
y Fj(Y)18363 13876 y Fq(b)p Fp(2)p Fq(\261)33 b(x)20372
12309 y Fx(\(1)296 b Fr(\241)f Fu(n)23928 12508 y Fq(b)24386
12309 y Fx(\))g Fr(\241)26649 11410 y Fx(1)p 26649 12003
651 54 v 26649 13220 a(2)27698 11047 y Fj(X)27653 13876
y Fq(b)p Fp(2)p Fq(\261)33 b(x)29883 12309 y Fu(n)30659
12508 y Fq(b)31413 12309 y Fx(+)32853 11410 y(1)p 32853
12003 V 32853 13220 a(4)34443 11047 y Fj(X)33857 13925
y Fq(p)p Fp(2)p Fq(P)131 b Fs(\()p Fq(x)p Fs(\))37345
11047 y Fj(Y)37168 13876 y Fq(b)p Fp(2)p Fq(@)52 b(p)39441
12309 y Fu(n)40217 12508 y Fq(b)45827 12309 y Fx(\(6\))4317
17938 y Fk(2.2)1793 b(Results)4317 20991 y Fx(W)-108
b(e)434 b(\257rst)f(pro)-36 b(v)g(e)433 b(existence.)4317
24563 y Fh(Theorem)499 b(1)1301 b FA(a\))466 b(The)e(fol)66
b(lowing)465 b(limits)f(exist)g(and)h(c)-66 b(oincide)11639
28470 y Fx(lim)11168 29301 y Fq(V)209 b Fp(!)p Fi(L)13456
29424 y Fo(1)14138 26597 y Fj(\277)16930 27571 y Fu(\302)-786
b(\302)g(\302)g(\302)p 15268 28164 4226 54 v 15268 29381
a Fr(j)p Fx(\244)16540 29580 y Fs(0)17065 29381 y Fx(\()p
Fu(V)289 b Fx(\))p Fr(j)19626 26597 y Fj(\300)20622 26894
y Fs(f)21256 28470 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))370 b(=)840 b(lim)27446 29301
y Fq(V)209 b Fp(!)p Fi(L)29734 29424 y Fo(1)30417 28470
y Fr(h)o Fu(\302)31748 28669 y Fs(0)32274 28470 y Fr(i)32791
27824 y Fs(f)33425 28470 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))369 b Fr(\264)h Fu(\302)40451
27922 y Fs(f)40863 28470 y Fx(\()p Fu(\257)74 b(;)221
b(q)48 b Fx(\))1937 b(\(7\))7569 32039 y FA(and)485 b(de\257ne)f(the)g
(me)-66 b(an)484 b(lo)-66 b(c)g(al)485 b(Euler)g(char)-66
b(acteristic)483 b(with)i(fr)-66 b(e)g(e)483 b(b)-66
b(oundary)485 b(c)-66 b(on-)7569 33644 y(dition)463 b
Fu(\302)12136 33162 y Fs(f)12549 33644 y Fx(\()p Fu(\257)74
b(;)221 b(q)48 b Fx(\))p FA(.)4967 36341 y(b\))466 b(A)-33
b(nalo)-66 b(gously,)464 b(the)g(fol)66 b(lowing)465
b(limits)f(exist)g(and)h(c)-66 b(oincide)10305 40014
y Fx(lim)9834 40846 y Fq(V)209 b Fp(!)p Fi(L)12122 40969
y Fo(1)12805 38141 y Fj(\277)15596 39116 y Fu(\302)-786
b(\302)g(\302)g(\302)p 13934 39709 V 13934 40926 a Fr(j)p
Fx(\244)15206 41125 y Fs(0)15731 40926 y Fx(\()p Fu(V)290
b Fx(\))p Fr(j)18292 38141 y Fj(\300)19288 38439 y Fs(w)20258
40014 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))370 b(=)840 b(lim)26447 40846 y Fq(V)209 b Fp(!)p
Fi(L)28735 40969 y Fo(1)29418 40014 y Fr(h)p Fu(\302)30750
40213 y Fs(0)31275 40014 y Fr(i)31792 39369 y Fs(w)32761
40014 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))370 b Fr(\264)f Fu(\302)39787 39466 y Fs(w)40535
40014 y Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))2265
b(\(8\))7569 43584 y FA(and)392 b(de\257ne)f(the)g(me)-66
b(an)391 b(lo)-66 b(c)g(al)392 b(Euler)g(char)-66 b(acteristic)390
b(with)i(wir)-66 b(e)g(d)391 b(b)-66 b(oundary)392 b(c)-66
b(on-)7569 45189 y(dition)463 b Fu(\302)12136 44707 y
Fs(w)12884 45189 y Fx(\()p Fu(\257)74 b(;)221 b(q)48
b Fx(\))p FA(.)6268 48761 y Fh(Pro)42 b(of.)1031 b Fx(The)585
b(pro)36 b(of)585 b(of)h(these)e(results)g(are)h(standard)f
(consequences)h(of)g(FK)-36 b(G)4317 50366 y(inequalities)435
b([FK)-36 b(G].)578 b(Let)433 b(us)h(\257rst)e(recall)j(basic)f
(de\257nitions)e(and)i(prop)36 b(erties.)4967 53938 y(A)434
b(con\257guration)f Fu(n)h Fx(dominates)g Fu(n)22460
53456 y Fp(0)22771 53938 y Fx(,)g Fu(n)369 b Fr(\302)g
Fu(n)26889 53456 y Fp(0)27200 53938 y Fx(,)434 b(if)g
Fu(n)29963 54137 y Fq(b)30790 53938 y Fr(\270)370 b Fu(n)32969
53456 y Fp(0)32969 54283 y Fq(b)33860 53938 y Fx(for)435
b(all)f(b)36 b(onds)433 b Fu(b)p Fx(.)4967 56634 y(A)488
b(function)f Fu(f)629 b Fx(is)488 b(said)f(to)h(b)36
b(e)487 b(increasing)h(if)g Fu(n)461 b Fr(\302)g Fu(n)31296
56152 y Fp(0)32094 56634 y Fr(\))488 b Fu(f)142 b Fx(\()p
Fu(n)p Fx(\))460 b Fr(\270)h Fu(f)142 b Fx(\()p Fu(n)40500
56152 y Fp(0)40811 56634 y Fx(\).)739 b(It)488 b(is)f(said)7569
58240 y(decreasing)434 b(if)g Fr(\241)p Fu(f)576 b Fx(is)433
b(increasing.)4967 60936 y(A)h(measure)f Fr(h)h(i)f Fx(is)h(said)f(to)h
(ha)-36 b(v)g(e)434 b(the)f(FK)-36 b(G)433 b(prop)36
b(ert)-36 b(y)433 b(if)h(:)23640 63815 y Fr(h)p Fu(f)142
b(g)48 b Fr(i)368 b(\270)h(h)p Fu(f)142 b Fr(ih)p Fu(g)48
b Fr(i)7569 66694 y Fx(for)434 b(all)g(increasing)g(functions)g
Fu(f)575 b Fx(and)433 b Fu(g)48 b Fx(.)25578 70015 y(6)p
eop
%%Page: 7 7
7 6 bop 6268 7306 a Fx(The)624 b(measures)f(\(5\))h(with)f(free)h(and)f
(wired)h(b)36 b(oundary)623 b(conditions)g(are)h(FK)-36
b(G,)4317 8911 y(see)564 b(e.g.)h(Theorem)g(2.2)f(in)g([A)-36
b(CCN)q(].)970 b(This)565 b(implies)f(the)g(follo)-36
b(wing)566 b(monotonicit)-36 b(y)4317 10516 y(prop)36
b(erties:)8547 13247 y Fr(h)p Fu(f)142 b Fr(i)10363 12602
y Fs(f)10998 13247 y Fx(\()p Fu(V)12551 12699 y Fp(0)12861
13247 y Fu(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))370
b Fr(\270)f(h)p Fu(f)142 b Fr(i)19552 12602 y Fs(f)20186
13247 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))p Fu(;)1523 b Fr(h)p Fu(f)142 b Fr(i)28325 12602
y Fs(w)29295 13247 y Fx(\()p Fu(V)30848 12699 y Fp(0)31159
13247 y Fu(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))369
b Fr(\267)g(h)p Fu(f)142 b Fr(i)37849 12602 y Fs(w)38819
13247 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))4317 15978 y(for)434 b(an)-36 b(y)434 b(increasing)g(function)f
(and)g(an)-36 b(y)434 b(pair)g(of)g(subsets)f Fu(V)34622
15496 y Fp(0)35302 15978 y Fr(\275)369 b Fu(V)289 b Fx(.)6268
18152 y(These)495 b(prop)36 b(erties)495 b(giv)-36 b(e,)512
b(b)-36 b(y)495 b(standard)f(argumen)-36 b(ts,)511 b(the)494
b(existence)i(of)g(the)f(in\257-)4317 19758 y(nite)438
b(v)-36 b(olume)438 b(limits)h(with)f(the)f(corresp)36
b(onding)437 b(b)36 b(oundary)438 b(conditions,)h(through)e(se-)4317
21363 y(quence)459 b(of)h(increasing)f(v)-36 b(olumes,)466
b(see)460 b(e.g.)g(Theorem)f(2.3)h(in)f([A)-36 b(CCN)q(].)655
b(They)459 b(imply)4317 22968 y(also,)514 b(follo)-36
b(wing)499 b([G],)513 b(that)496 b(b)36 b(oth)496 b(limiting)i(states)f
(are)g(translation)g(in)-36 b(v)-72 b(arian)-36 b(t.)768
b(The)4317 24573 y(translation)425 b(in)-36 b(v)-72 b(ariance)424
b(allo)-36 b(ws)426 b(\257nally)f(to)f(sho)-36 b(w)425
b(that)f(the)f(t)-36 b(w)g(o)425 b(limits)g(in)f(\(7\))g(\(resp.)4317
26178 y(\(8\)\))343 b(coincide)h(pro)-36 b(vided)343
b(the)f(\257rst)h(one)g(is)h(tak)-36 b(en)343 b(in)g(suc)-36
b(h)343 b(a)g(w)-36 b(a)g(y)344 b(that)f Fr(j)p Fu(B)67
b Fx(\()p Fu(V)290 b Fx(\))p Fu(=V)f Fr(j)369 b(!)g Fx(0)4317
27783 y(as)434 b Fu(V)658 b Fr(!)370 b Ft(L)9914 27982
y Fs(1)10439 27783 y Fx(.)p 11812 27783 651 651 v 4317
31165 a Fh(Theorem)499 b(2)1301 b FA(a\))605 b(The)f(me)-66
b(an)603 b(lo)-66 b(c)g(al)604 b(Euler)g(char)-66 b(acteristics)603
b(satis\257es)h(the)g(duality)7569 32770 y(r)-66 b(elation)21453
34375 y Fu(\302)22268 33827 y Fs(f)22680 34375 y Fx(\()p
Fu(\257)74 b(;)221 b(q)48 b Fx(\))369 b(=)f Fr(\241)p
Fu(\302)29304 33827 y Fs(w)30052 34375 y Fx(\()p Fu(\257)31366
33827 y Fp(\244)31892 34375 y Fu(;)221 b(q)48 b Fx(\))12222
b(\(9\))7569 36613 y FA(wher)-66 b(e)464 b(the)h(dual)h(inverse)d(temp)
-66 b(er)g(atur)g(e)463 b Fu(\257)28601 36131 y Fp(\244)29127
36613 y FA(is)i(given)e(by)21585 39344 y Fx(\()p Fu(e)22694
38796 y Fq(\257)23617 39344 y Fr(\241)296 b Fx(1\)\()p
Fu(e)27211 38796 y Fq(\257)27785 38483 y Fm(\244)28614
39344 y Fr(\241)g Fx(1\))369 b(=)f Fu(q)11751 b Fx(\(10\))4967
42600 y FA(b\))493 b(A)-33 b(t)491 b(the)h(self-dual)h(p)-66
b(oint)492 b Fu(\257)19856 42799 y Fq(t)20671 42600 y
Fx(=)419 b(log)19 b(\(1)316 b(+)26581 41772 y Fr(p)p
27688 41772 625 54 v 828 x Fu(q)48 b Fx(\))492 b FA(solution)g(of)g
(\(10\))i(with)e Fu(\257)i Fx(=)419 b Fu(\257)45009 42118
y Fp(\244)46027 42600 y FA(we)7569 44205 y(have)21394
45810 y Fu(\302)22209 45262 y Fs(f)22622 45810 y Fx(\()p
Fu(\257)23862 46009 y Fq(t)24257 45810 y Fu(;)221 b(q)48
b Fx(\))369 b(=)f Fr(\241)p Fu(\302)29567 45262 y Fs(w)30315
45810 y Fx(\()p Fu(\257)31555 46009 y Fq(t)31951 45810
y Fu(;)221 b(q)48 b Fx(\))11512 b(\(11\))6268 49825 y
Fh(Pro)42 b(of.)556 b Fx(Dualit)-36 b(y)367 b(prop)36
b(erties)365 b(b)36 b(et)-36 b(w)g(een)366 b(FK)f(measures)h(with)g
(free)h(and)e(wired)h(b.c.)4317 51430 y(ha)-36 b(v)g(e)431
b(b)36 b(een)430 b(already)h(deriv)-36 b(ed)431 b(in)f(more)h(general)g
(situation,)g(\(see)g([PV]\),)g(and)f(w)-36 b(e)431 b(will)4317
53035 y(use)587 b(some)h(notations)f(inspired)g(from)h(Section)f(3.3)h
(of)h(that)e(reference.)1039 b(First,)626 b(w)-36 b(e)4317
54640 y(recall)473 b(some)g(basic)f(geometrical)i(results)e(ab)36
b(out)472 b(P)-36 b(oincar)g(\266)-614 b(e)472 b(dualit)-36
b(y)473 b(and)e(Alexander)4317 56245 y(dualit)-36 b(y)-108
b(.)578 b(Namely)-108 b(,)435 b(w)-36 b(e)434 b(in)-36
b(tro)36 b(duce)433 b(the)g(dual)g(lattice)13005 58976
y(\()p Ft(Z)14397 58428 y Fs(2)14922 58976 y Fx(\))15428
58428 y Fp(\244)16322 58976 y Fx(=)369 b Fr(f)p Fu(x)g
Fx(=)g(\()p Fu(x)22101 59175 y Fs(1)22627 58976 y Fu(;)221
b(x)23948 59175 y Fs(2)24474 58976 y Fx(\))369 b(:)g
Fu(x)26818 59175 y Fq(i)27489 58976 y Fx(+)295 b(1)p
Fu(=)p Fx(2)370 b Fr(2)f Ft(Z)p Fu(;)442 b(i)369 b Fx(=)g(1)p
Fu(;)221 b Fx(2)p Fr(g)4317 61707 y Fx(and)378 b(use)g
Ft(L)9869 61225 y Fp(\244)10773 61707 y Fx(to)h(denote)e(the)h(corresp)
36 b(onding)378 b(cell)i(complex.)560 b Ft(L)35651 61225
y Fp(\244)36555 61707 y Fx(is)379 b(the)f(dual)g(complex)4317
63313 y(of)434 b Ft(L)g Fx(and)f(the)g(follo)-36 b(wing)435
b(geometrical)g(relations)f(hold:)5907 66694 y(1.)651
b(eac)-36 b(h)433 b(site)h Fu(x)369 b Fr(2)g Ft(L)433
b Fx(is)h(the)f(cen)-36 b(ter)433 b(of)h(a)g(unique)f(plaquette)h
Fu(p)37173 66212 y Fp(\244)38067 66694 y Fr(2)369 b Ft(L)40208
66212 y Fp(\244)40733 66694 y Fx(,)25578 70015 y(7)p
eop
%%Page: 8 8
8 7 bop 5907 7306 a Fx(2.)651 b(eac)-36 b(h)433 b(b)36
b(ond)433 b Fu(b)369 b Fr(2)g Ft(L)433 b Fx(is)h(crossed)f(b)-36
b(y)434 b(a)g(unique)f(b)36 b(ond)432 b Fu(b)34039 6824
y Fp(\244)34934 7306 y Fr(2)369 b Ft(L)37075 6824 y Fp(\244)37600
7306 y Fx(,)5907 9893 y(3.)651 b(eac)-36 b(h)433 b(plaquette)h
Fu(p)369 b Fr(2)f Ft(L)433 b Fx(has)h(a)g(unique)f(site)h
Fu(x)30597 9411 y Fp(\244)31492 9893 y Fr(2)368 b Ft(L)33632
9411 y Fp(\244)34591 9893 y Fx(at)434 b(its)g(cen)-36
b(ter.)6268 12972 y(This)428 b(corresp)36 b(ondence)427
b(b)36 b(et)-36 b(w)g(een)426 b(the)h Fu(p)p Fx({cells)i(of)f
Ft(L)f Fx(and)g(the)g(\(2)283 b Fr(\241)g Fu(p)p Fx(\){cells)428
b(of)g Ft(L)46963 12490 y Fp(\244)4317 14577 y Fx(is)434
b(one{to{one)22573 16182 y Fu(s)23186 16381 y Fq(p)24084
16182 y Fr(\303)-221 b(!)369 b Fu(s)27501 15634 y Fp(\244)27501
16510 y Fs(2)p Fp(\241)p Fq(p)45176 16182 y Fx(\(12\))4317
18319 y(F)-108 b(or)403 b(a)g(sub)36 b(complex)403 b(\244)369
b Fr(\275)g Ft(L)p Fu(;)403 b Fx(the)g(dual)g(\244)25025
17837 y Fp(\244)25953 18319 y Fx(of)h(\244)f(is)g(the)g(set)g(of)h
(elemen)-36 b(ts)403 b(of)g Ft(L)43272 17837 y Fp(\244)44201
18319 y Fx(whic)-36 b(h)4317 19924 y(are)434 b(in)f(one)h(to)g(one)f
(corresp)36 b(ondence)433 b(\(12\))h(with)f(the)g(elemen)-36
b(ts)434 b(of)g(\244.)6268 22064 y(Consider)g(the)f(set)g(of)i(b)36
b(onds)432 b Fu(V)659 b Fr(\275)369 b Ft(L)24952 22263
y Fs(1)25911 22064 y Fx(suc)-36 b(h)433 b(that)13485
24560 y(\244)14388 24759 y Fs(0)14914 24560 y Fx(\()p
Fu(V)289 b Fx(\))369 b(=)18722 23484 y Fj(\251)19497
24560 y Fx(\()p Fu(x)20742 24759 y Fs(1)21268 24560 y
Fu(;)221 b(x)22589 24759 y Fs(2)23116 24560 y Fx(\))368
b Fr(2)h Ft(Z)26131 24012 y Fs(2)27025 24560 y Fx(:)h
Fr(j)p Fu(x)28864 24759 y Fq(i)29239 24560 y Fr(j)f(\267)h
Fu(m;)590 b(i)369 b Fx(=)f(1)p Fu(;)221 b Fx(2)37544
23484 y Fj(\252)4317 27056 y Fx(The)500 b(dual)g(set)g([)q(\244\()p
Fu(V)289 b Fx(\)])15796 26410 y Fp(\244)16822 27056 y
Fx(is)500 b(the)g(union)f([)q(\244\()p Fu(V)289 b Fx(\)])27867
26410 y Fp(\244)28875 27056 y Fx(=)482 b Fr([)31255 26574
y Fs(2)31255 27384 y Fq(p)p Fs(=0)32986 27056 y Fx(\244)33889
26574 y Fp(\244)33889 27384 y Fq(p)34417 27056 y Fx(\()p
Fu(V)290 b Fx(\))499 b(where)i(eac)-36 b(h)500 b Fu(p)p
Fx({cells)4317 28661 y Fu(s)4930 28179 y Fp(\244)4930
28989 y Fq(p)5828 28661 y Fr(2)368 b Fx(\244)7985 28179
y Fp(\244)7985 28989 y Fq(p)8514 28661 y Fx(\()p Fu(V)289
b Fx(\))366 b(is)g(in)g(one)g(-to-one)f(corresp)36 b(ondence)365
b(with)h(a)h(2)157 b Fr(\241)g Fu(p)366 b Fx(cell)h Fu(s)39080
28860 y Fs(2)p Fp(\241)p Fq(p)41180 28661 y Fr(2)h Fx(\244)43337
28860 y Fs(2)p Fp(\241)p Fq(p)45068 28661 y Fx(\()p Fu(V)289
b Fx(\).)4317 30266 y(In)434 b(particular)20124 30742
y Fj(\257)20124 31539 y(\257)20567 31871 y Fx(\244)21470
31323 y Fp(\244)21470 32199 y Fq(p)21999 31871 y Fx(\()p
Fu(V)289 b Fx(\))24058 30742 y Fj(\257)24058 31539 y(\257)24870
31871 y Fx(=)368 b Fr(j)p Fx(\244)27522 32070 y Fs(2)p
Fp(\241)p Fq(p)29253 31871 y Fx(\()p Fu(V)289 b Fx(\))p
Fr(j)13495 b Fx(\(13\))6268 34543 y(W)-108 b(e)583 b(let)g(\255)624
b(=)e(\244\()p Fu(V)289 b Fx(\))397 b Fr([)f Fu(f)725
b Fx(b)36 b(e)583 b(the)f(complex)i(obtained)e(from)h(\244\()p
Fu(V)289 b Fx(\))583 b(b)-36 b(y)583 b(adding)4317 36148
y(an)576 b(extra)h(face)g Fu(f)718 b Fx(whose)576 b(b)36
b(oundary)575 b(is)i(the)e(set)h(of)h(b)36 b(onds)575
b(of)i Fu(B)67 b Fx(\()p Fu(V)290 b Fx(\).)1005 b(Then)576
b(\255)g(is)4317 37753 y(homeomorphic)433 b(to)h(the)f(sphere)g
Fu(S)21821 37271 y Fs(2)22347 37753 y Fx(.)578 b(W)-108
b(e)434 b(let)g Fu(x)28144 37271 y Fp(\244)29103 37753
y Fx(b)36 b(e)434 b(some)f(p)36 b(oin)-36 b(t)434 b(inside)f(the)g
(face)i Fu(f)142 b Fx(.)6268 39894 y(W)-108 b(e)506 b(de\257ne)e(the)h
(dual)g(\255)18622 39412 y Fp(\244)19654 39894 y Fx(of)h(\255)g(as)g
(the)f(set)g([\244\()p Fu(V)289 b Fx(\)])32419 39248
y Fp(\244)33289 39894 y Fr([)344 b Fu(x)35258 39412 y
Fp(\244)36289 39894 y Fx(except)506 b(that)f(no)-36 b(w)506
b(all)4317 41499 y(the)e(b)36 b(onds)503 b(of)i(\244)12954
41017 y Fp(\244)12954 41827 y Fs(1)13479 41499 y Fx(\()p
Fu(V)289 b Fx(\))504 b(that)g(crosses)g Fu(B)67 b Fx(\()p
Fu(V)289 b Fx(\))504 b(meet)g(at)g(the)f(p)36 b(oin)-36
b(t)504 b Fu(x)38330 41017 y Fp(\244)38856 41499 y Fx(.)790
b(W)-108 b(e)504 b(call)h(faces)4317 43104 y(of)448 b(\255)6751
42622 y Fp(\244)7724 43104 y Fx(the)e(new)h(2{cells.)619
b(Again)448 b(the)e(corresp)36 b(ondence)446 b(is)h(one-to-one)f(pro)
-36 b(vided)447 b(one)4317 44709 y(replaces)434 b(2{cells)h(b)-36
b(y)433 b(faces.)6268 46849 y(W)-108 b(e)434 b(no)-36
b(w)433 b(turn)g(to)g(Alexander's)i(dualit)-36 b(y)-108
b(.)578 b(Let)433 b Fu(n)369 b Fr(2)g(f)p Fx(0)p Fu(;)221
b Fx(1)p Fr(g)35531 46367 y Fq(V)36779 46849 y Fx(and)17769
49345 y Fu(V)18816 48796 y Fp(\244)19711 49345 y Fx(=)368
b Fr(f)q Fu(b)22309 48796 y Fp(\244)23203 49345 y Fr(2)h
Fx(\255)25397 48796 y Fp(\244)26292 49345 y Fx(:)g Fu(b)27575
48796 y Fp(\244)28535 49345 y Fx(crosses)434 b Fu(b)p
Fr(g)4317 51841 y Fx(W)-108 b(e)434 b(de\257ne)e(the)h(A-dual)g
(con\257guration)453 b Fj(b)-758 b Fu(n)370 b Fr(2)e(f)p
Fx(0)p Fu(;)221 b Fx(1)p Fr(g)30339 51359 y Fq(V)31098
51046 y Fm(\244)31633 51841 y Fx(of)434 b Fu(n)g Fx(b)-36
b(y)22436 54336 y Fj(b)-757 b Fu(n)23193 54535 y Fq(b)23596
54283 y Fm(\244)24500 54336 y Fx(=)369 b(1)295 b Fr(\241)g
Fu(n)28930 54535 y Fq(b)45176 54336 y Fx(\(14\))4317
56832 y(where)482 b Fu(b)8676 56350 y Fp(\244)9684 56832
y Fx(is)h(the)f(b)36 b(ond)481 b(of)i Fu(V)19243 56350
y Fp(\244)20252 56832 y Fx(in)-36 b(tersecting)481 b
Fu(b)p Fx(.)725 b(In)482 b(other)g(w)-36 b(ords,)495
b(if)483 b(w)-36 b(e)482 b(let)g Fu(X)557 b Fr(\275)452
b Fu(V)4317 58437 y Fx(b)36 b(e)405 b(the)g(set)h(of)g(b)36
b(onds)405 b Fu(b)g Fx(suc)-36 b(h)405 b(that)g Fu(n)22930
58636 y Fq(b)23757 58437 y Fx(=)369 b(1,)412 b(\244\()p
Fu(X)104 b Fx(\))405 b(its)h(asso)36 b(ciated)407 b(cell-complex)f(and)
4400 59839 y Fj(b)4317 60175 y Fx(\244\()p Fu(X)104 b
Fx(\))521 b(=)g([\255)356 b Fr(n)g Fx(\244\()p Fu(X)104
b Fx(\)])15604 59693 y Fp(\244)16131 60175 y Fx(,)545
b(then)522 b(the)g(b)36 b(onds)522 b(of)27961 59839 y
Fj(b)27878 60175 y Fx(\244\()p Fu(X)104 b Fx(\))523 b(are)g(those)g(of)
g(\255)39758 59693 y Fp(\244)40807 60175 y Fx(that)f(do)h(not)4317
61780 y(in)-36 b(tersect)433 b(the)g(b)36 b(onds)433
b(of)h(\244\()p Fu(X)104 b Fx(\).)579 b(Ob)-36 b(viously)434
b(one)g(has)13380 64276 y Fu(N)14561 63727 y Fs(1)15086
64276 y Fx(\()p Fu(n)p Fx(\))296 b(+)e Fu(N)19657 63727
y Fs(1)20183 64276 y Fx(\()19 b Fj(b)-757 b Fu(n)p Fx(\))369
b(=)f Fr(j)p Fx(\244)24992 64475 y Fs(1)25518 64276 y
Fx(\()p Fu(V)289 b Fx(\))p Fr(j)369 b Fx(=)f Fr(j)p Fx(\244)30967
63727 y Fp(\244)30967 64604 y Fs(1)31493 64276 y Fx(\()p
Fu(V)289 b Fx(\))p Fr(j)11255 b Fx(\(15\))13380 66213
y Fu(N)14561 65664 y Fs(2)15086 66213 y Fx(\()p Fu(n)p
Fx(\))296 b(+)e Fu(N)19657 65664 y Fs(0)20183 66213 y
Fx(\()19 b Fj(b)-757 b Fu(n)p Fx(\))369 b(=)f Fr(j)p
Fx(\244)24992 66412 y Fs(2)25518 66213 y Fx(\()p Fu(V)289
b Fx(\))p Fr(j)295 b Fx(+)g(1)369 b(=)g Fr(j)p Fx(\244)33220
65664 y Fp(\244)33220 66541 y Fs(0)33745 66213 y Fx(\()p
Fu(V)289 b Fx(\))p Fr(j)295 b Fx(+)g(1)6751 b(\(16\))25578
70015 y(8)p eop
%%Page: 9 9
9 8 bop 4317 7306 a Fx(where)339 b Fu(N)9161 6824 y Fq(p)9689
7306 y Fx(\()19 b Fj(b)-757 b Fu(n)p Fx(\))339 b(denote)f(the)h(n)-36
b(um)g(b)36 b(er)337 b(of)j Fu(p)p Fx({cells)f(of)29585
6970 y Fj(b)29503 7306 y Fx(\244\()p Fu(X)104 b Fx(\).)547
b(Moreo)-36 b(v)g(er)339 b(b)-36 b(y)339 b(Alexander's)4317
8911 y(dualit)-36 b(y)434 b(theorem,)f(see)h([A])g(\(Theorem)g(4.10)h
(p.)578 b(24\),)434 b([Le])g(\(p.)578 b(205\),)434 b(or)g([PV]:)20803
11502 y Fu(\274)21589 10953 y Fs(0)22114 11502 y Fx(\()p
Fu(n)p Fx(\))369 b(=)f Fu(\274)26437 10953 y Fs(1)26963
11502 y Fx(\()19 b Fj(b)-757 b Fu(n)p Fx(\))295 b(+)g(1)14173
b(\(17\))20803 13439 y Fu(\274)21589 12890 y Fs(0)22114
13439 y Fx(\()19 b Fj(b)-757 b Fu(n)p Fx(\))369 b(=)f
Fu(\274)26437 12890 y Fs(1)26963 13439 y Fx(\()p Fu(n)p
Fx(\))295 b(+)g(1)14173 b(\(18\))4317 16312 y(where)555
b Fu(\274)8982 15830 y Fq(p)9510 16312 y Fx(\()19 b Fj(b)-757
b Fu(n)q Fx(\))554 b(denotes)h(the)f Fu(p)p Fx({Betti)h(n)-36
b(um)g(b)36 b(er)554 b(of)i(the)e(complex)37887 15976
y Fj(b)37805 16312 y Fx(\244)o(\()p Fu(X)104 b Fx(\).)943
b(Then,)586 b(b)-36 b(y)4317 17917 y(using)434 b(successiv)-36
b(ely)434 b(\(15\),)h(\(10\))e(and)h(Euler's)f(form)-36
b(ula)434 b(\(2\))g(\(3\))f(w)-36 b(e)434 b(can)g(write)5645
20987 y Fj(\241)6254 22063 y Fu(e)6857 21515 y Fq(\257)7781
22063 y Fr(\241)296 b Fx(1)9760 20987 y Fj(\242)10369
21250 y Fq(N)11210 20938 y Fo(1)11671 21250 y Fs(\()p
Fq(n)p Fs(\))13251 22063 y Fu(q)13876 21515 y Fp(j)o
Fs(\244)14789 21638 y Fo(0)15250 21515 y Fs(\()p Fq(V)209
b Fs(\))p Fp(j\241)p Fq(N)18573 21202 y Fo(0)19034 21515
y Fs(\()p Fq(n)p Fs(\)+)p Fq(\274)21641 21202 y Fo(0)22102
21515 y Fs(\()p Fq(n)p Fs(\))23829 22063 y Fx(=)25210
20190 y Fj(\265)26321 21165 y Fu(e)26924 20683 y Fq(\257)27847
21165 y Fr(\241)296 b Fx(1)p 26321 21758 3506 54 v 27761
22974 a Fu(q)29959 20190 y Fj(\266)30937 20418 y Fq(N)31778
20106 y Fo(1)32239 20418 y Fs(\()p Fq(n)p Fs(\))33819
22063 y Fu(q)34444 21515 y Fp(j)o Fs(\244)35357 21638
y Fo(0)35818 21515 y Fs(\()p Fq(V)209 b Fs(\))p Fp(j\241)p
Fq(N)39141 21202 y Fo(0)39603 21515 y Fs(\()p Fq(n)p
Fs(\)+)p Fq(\274)42210 21202 y Fo(0)42670 21515 y Fs(\()p
Fq(n)p Fs(\)+)p Fq(N)45546 21202 y Fo(1)46007 21515 y
Fs(\()p Fq(n)p Fs(\))9389 26154 y Fx(=)10770 24281 y
Fj(\265)11880 25255 y Fu(e)12483 24773 y Fq(\257)13407
25255 y Fr(\241)295 b Fx(1)p 11880 25848 V 13321 27065
a Fu(q)15519 24281 y Fj(\266)16496 24509 y Fp(j)q Fs(\244)17411
24632 y Fo(1)17871 24509 y Fs(\()p Fq(V)209 b Fs(\))p
Fp(j)19898 24281 y Fj(\265)21009 25255 y Fu(e)21612 24773
y Fq(\257)22536 25255 y Fr(\241)295 b Fx(1)p 21009 25848
V 22450 27065 a Fu(q)24647 24281 y Fj(\266)25625 24509
y Fp(\241)p Fq(N)27198 24196 y Fo(1)27659 24509 y Fs(\()24
b Fg(b)-547 b Fq(n)p Fs(\))29239 26154 y Fu(q)29864 25605
y Fp(j)p Fs(\244)30778 25728 y Fo(0)31238 25605 y Fs(\()p
Fq(V)209 b Fs(\))p Fp(j)q(\241)p Fq(N)34562 25293 y Fo(0)35023
25605 y Fs(\()p Fq(n)p Fs(\)+)p Fq(\274)37630 25293 y
Fo(0)38091 25605 y Fs(\()p Fq(n)p Fs(\)+)p Fq(N)40967
25293 y Fo(1)41428 25605 y Fs(\()p Fq(n)p Fs(\))9891
30168 y Fx(=)11271 28295 y Fj(\265)12382 29269 y Fu(e)12985
28787 y Fq(\257)13909 29269 y Fr(\241)295 b Fx(1)p 12382
29862 V 13823 31079 a Fu(q)16020 28295 y Fj(\266)16998
28523 y Fp(j)p Fs(\244)17912 28646 y Fo(1)18373 28523
y Fs(\()p Fq(V)209 b Fs(\))p Fp(j)20400 30168 y Fu(q)21025
29619 y Fp(j)p Fs(\244)21939 29742 y Fo(0)22400 29619
y Fs(\()p Fq(V)g Fs(\))p Fp(j)24205 30168 y Fx(\()p Fu(e)25314
29619 y Fq(\257)25888 29307 y Fm(\244)26718 30168 y Fr(\241)295
b Fx(1\))29202 29619 y Fq(N)30043 29307 y Fo(1)30504
29619 y Fs(\()24 b Fg(b)-547 b Fq(n)p Fs(\))31863 30168
y Fu(q)32488 29619 y Fp(\241)p Fq(N)34061 29307 y Fo(0)34521
29619 y Fs(\()p Fq(n)p Fs(\)+)p Fq(\274)37128 29307 y
Fo(0)37589 29619 y Fs(\()p Fq(n)p Fs(\)+)p Fq(N)40465
29307 y Fo(1)40926 29619 y Fs(\()p Fq(n)p Fs(\))18057
34182 y Fx(=)19438 32309 y Fj(\265)20548 33283 y Fu(e)21151
32801 y Fq(\257)22075 33283 y Fr(\241)296 b Fx(1)p 20548
33876 V 21989 35093 a Fu(q)24187 32309 y Fj(\266)25164
32537 y Fp(j)q Fs(\244)26079 32660 y Fo(1)26540 32537
y Fs(\()p Fq(V)209 b Fs(\))p Fp(j)28567 34182 y Fu(q)29192
33633 y Fp(j)o Fs(\244)30105 33756 y Fo(0)30566 33633
y Fs(\()p Fq(V)g Fs(\))p Fp(j)32372 34182 y Fx(\()p Fu(e)33481
33633 y Fq(\257)34055 33321 y Fm(\244)34884 34182 y Fr(\241)295
b Fx(1\))37368 33633 y Fq(N)38209 33321 y Fo(1)38671
33633 y Fs(\()24 b Fg(b)-547 b Fq(n)p Fs(\))40029 34182
y Fu(q)40654 33633 y Fq(N)41495 33321 y Fo(2)41956 33633
y Fs(\()p Fq(n)p Fs(\)+)p Fq(\274)44563 33321 y Fo(1)45024
33633 y Fs(\()p Fq(n)p Fs(\))4317 38381 y Fx(Setting)433
b Fu(R)380 b Fx(=)11548 36907 y Fj(\263)12474 37858 y
Fq(e)12910 37546 y Fn(\257)13463 37858 y Fp(\241)p Fs(1)p
12474 38076 2192 54 v 13344 38839 a Fq(q)14799 36907
y Fj(\264)15592 37204 y Fp(j)p Fs(\244)16506 37327 y
Fo(1)16967 37204 y Fs(\()p Fq(V)209 b Fs(\))p Fp(j)18994
38381 y Fu(q)19619 37899 y Fp(j)p Fs(\244)20533 38022
y Fo(0)20993 37899 y Fs(\()p Fq(V)g Fs(\))p Fp(j)22799
38381 y Fx(,)434 b(w)-36 b(e)434 b(get)g(from)g(\(16\)\(18\))5830
41895 y Fu(R)6831 41346 y Fp(\241)p Fs(1)8310 40819 y
Fj(\241)8919 41895 y Fu(e)9522 41346 y Fq(\257)10446
41895 y Fr(\241)295 b Fx(1)12424 40819 y Fj(\242)13033
41082 y Fq(N)13874 40769 y Fo(1)14336 41082 y Fs(\()p
Fq(n)p Fs(\))15915 41895 y Fu(q)16540 41346 y Fp(j)p
Fs(\244)17454 41469 y Fo(0)17915 41346 y Fs(\()p Fq(V)209
b Fs(\))p Fp(j\241)p Fq(N)21238 41034 y Fo(0)21699 41346
y Fs(\()p Fq(n)p Fs(\)+)p Fq(\274)24306 41034 y Fo(0)24767
41346 y Fs(\()p Fq(n)p Fs(\))26494 41895 y Fx(=)369 b(\()p
Fu(e)28984 41346 y Fq(\257)29558 41034 y Fm(\244)30387
41895 y Fr(\241)295 b Fx(1\))32871 41346 y Fq(N)33712
41034 y Fo(1)34174 41346 y Fs(\()24 b Fg(b)-547 b Fq(n)p
Fs(\))35532 41895 y Fu(q)36157 41419 y Fr(j)36525 41309
y Fs(\244)37178 40996 y Fm(\244)37178 41584 y Fo(0)37657
41309 y Fs(\()p Fq(V)209 b Fs(\))39146 41420 y Fr(j)39515
41309 y Fp(\241)p Fq(N)41088 40996 y Fo(0)41550 41309
y Fs(\()24 b Fg(b)-547 b Fq(n)o Fs(\)+)p Fq(\274)44156
40996 y Fo(0)44617 41309 y Fs(\()24 b Fg(b)-547 b Fq(n)p
Fs(\))45176 43500 y Fx(\(19\))4317 45105 y(This)323 b(form)-36
b(ula)324 b(establishes)f(the)f(one-to-one)g(corresp)36
b(ondence)322 b(b)36 b(et)-36 b(w)g(een)323 b(the)f(FK)h(mea-)4317
46710 y(sures)508 b(with)g(free)h(and)e(wired)i(b.c.:)728
b(indeed,)526 b(the)508 b(righ)-36 b(t-hand-side)506
b(of)j(\(19\))f(coincide)4317 48315 y(up)415 b(to)g(a)h(b)36
b(oundary)414 b(term)h(indep)36 b(enden)-36 b(t)413 b(of)435
b Fj(b)-757 b Fu(n)416 b Fx(with)f(the)g(Boltzman)h(w)-36
b(eigh)g(t)415 b(en)-36 b(tering)4317 49920 y(in)371
b(the)f(de\257nition)g(of)i(the)e(partition)h(function)f(\(4\))h(with)g
(wired)g(b)36 b(oundary)370 b(condition.)4317 51525 y(F)-108
b(rom)433 b(this)g(form)-36 b(ula,)435 b(w)-36 b(e)434
b(get)f(b)-36 b(y)434 b(\(17)g(\)\(18\):)16081 54116
y Fr(h)o Fu(\302)-786 b(\302)g(\302)g(\302)p Fr(i)18015
53470 y Fs(f)18650 54116 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))369 b(=)g Fr(h)p Fx(2)295 b Fr(\241)g
Fu(\302)-786 b(\302)g(\302)g(\302)p Fr(i)29048 53470
y Fs(w)30017 54116 y Fx(\()p Fu(V)31570 53567 y Fp(\244)32096
54116 y Fu(;)221 b(\257)33486 53567 y Fp(\244)34012 54116
y Fu(;)g(q)48 b Fx(\))4317 56707 y(It)429 b(then)f(su\261ces)g(to)h
(divide)h(b)36 b(oth)428 b(terms)g(of)i(this)e(equation)i(b)-36
b(y)428 b Fr(j)p Fx(\244)37612 56906 y Fs(0)38138 56707
y Fx(\()p Fu(V)289 b Fx(\))p Fr(j)429 b Fx(and)f(to)h(tak)-36
b(e)4317 58312 y(the)433 b(thermo)36 b(dynamic)434 b(limit)g(\()p
Fu(m)368 b Fr(!)i(1)p Fx(\))433 b(to)h(get)g(the)f(result.)p
35520 58312 651 651 v 4317 61513 a Fh(Remark)499 b(3)650
b FA(L)-66 b(et)464 b(us)i(mention)d(that)h(for)h(every)f
Fu(\257)443 b Fr(6)p Fx(=)369 b Fu(\257)31859 61712 y
Fq(t)20606 64104 y Fu(\302)21421 63555 y Fs(f)21834 64104
y Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))368 b(=)h
Fu(\302)27425 63555 y Fs(w)28173 64104 y Fx(\()p Fu(\257)74
b(;)221 b(q)48 b Fx(\))13976 b(\(20\))4317 66694 y FA(when)465
b Fu(q)416 b Fx(=)369 b(2)465 b FA(and)g Fu(q)416 b Fr(\270)370
b Fx(4)25578 70015 y(9)p eop
%%Page: 10 10
10 9 bop 6268 7306 a Fx(This)296 b(is)g(a)f(consequence)h(of)g(the)f
(di\256eren)-36 b(tiabilit)g(y)295 b(of)h(the)f(free)h(energy)g(with)f
(resp)36 b(ect)4317 8911 y(to)501 b Fu(\257)576 b Fx(for)501
b(the)g(corresp)36 b(onding)501 b(v)-72 b(alues)502 b(of)g
Fu(q)548 b Fx(com)-36 b(bined)501 b(with)g(FK)-36 b(G)500
b(inequalit)-36 b(y)-108 b(,)520 b(\(see)4317 10516 y([LM]\).)6268
12643 y(Actually)435 b(b)-36 b(y)433 b(FK)-36 b(G)433
b(inequalit)-36 b(y)-108 b(,)435 b(one)e(has)h(that)11845
13824 y Fj(8)11845 15020 y(>)11845 15418 y(>)11845 15817
y(<)11845 18208 y(>)11845 18606 y(>)11845 19005 y(:)13427
14976 y Fr(h)p Fu(n)14720 15175 y Fq(b)15178 14976 y
Fr(i)15695 14427 y Fs(f)16107 14976 y Fx(\()p Fu(V)72
b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))370 b Fr(\267)f(h)p
Fu(n)23611 15175 y Fq(b)24069 14976 y Fr(i)24586 14427
y Fs(b)26 b(c)25608 14976 y Fx(\()p Fu(V)72 b(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))370 b Fr(\267)f(h)p Fu(n)33112
15175 y Fq(b)33570 14976 y Fr(i)34087 14427 y Fs(w)34834
14976 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))13427 18457 y(0)369 b Fr(\267)g(h)16384 17195
y Fj(Y)16365 20024 y Fq(b)p Fp(2)p Fq(A)18321 18457 y
Fu(n)19097 18656 y Fq(b)19555 18457 y Fr(i)20072 17909
y Fs(w)21115 18457 y Fr(\241)295 b(h)22979 17195 y Fj(Y)22960
20024 y Fq(b)p Fp(2)p Fq(A)24916 18457 y Fu(n)25692 18656
y Fq(b)26150 18457 y Fr(i)369 b(\267)28438 17195 y Fj(X)28530
20024 y Fq(b)p Fp(2)p Fq(A)30578 17381 y Fj(\241)31187
18457 y Fr(h)p Fu(n)32480 18656 y Fq(b)32938 18457 y
Fr(i)33455 17909 y Fs(w)34497 18457 y Fr(\241)296 b(h)p
Fu(n)37119 18656 y Fq(b)37576 18457 y Fr(i)38093 17381
y Fj(\242)4317 22046 y Fx(since)419 b(ob)-36 b(viously)420
b Fu(n)14002 22245 y Fq(b)14880 22046 y Fx(is)f(an)g(increasing)g
(function)g(and)f(the)h(same)g(is)g(also)h(true)f(for)g(the)4317
23651 y(function)433 b Fu(f)10052 23850 y Fq(A)11182
23651 y Fx(=)12562 22654 y Fj(P)13964 24038 y Fq(b)p
Fp(2)p Fq(A)15976 23651 y Fu(n)16752 23850 y Fq(b)17505
23651 y Fr(\241)18833 22654 y Fj(Q)20088 24038 y Fq(b)p
Fp(2)p Fq(A)22099 23651 y Fu(n)22875 23850 y Fq(b)23334
23651 y Fx(,)g(\(see)h(again)g([LM]\).)6268 25778 y(Therefore)585
b(the)f(state)g(is)g(unique)g(as)h(so)36 b(on)584 b(as,)623
b(in)584 b(the)g(thermo)36 b(dynamic)584 b(limit,)4317
27383 y Fr(h)p Fu(n)5610 27582 y Fq(b)6068 27383 y Fr(i)6585
26901 y Fs(f)6997 27383 y Fx(\()p Fu(\257)74 b(;)221
b(q)48 b Fx(\))569 b(=)g Fr(h)p Fu(n)13467 27582 y Fq(b)13925
27383 y Fr(i)14442 26901 y Fs(w)15190 27383 y Fx(\()p
Fu(\257)74 b(;)221 b(q)48 b Fx(\).)931 b(This)552 b(prop)36
b(ert)-36 b(y)551 b(holds)g(whenev)-36 b(er)551 b(the)g(free)h(energy)f
(is)4317 28988 y(di\256eren)-36 b(tiable)433 b(with)h(resp)36
b(ect)433 b(to)h Fu(\257)74 b Fx(.)6268 31116 y(Indeed,)468
b(again)461 b(b)-36 b(y)461 b(FK)-36 b(G,)461 b Fr(h)p
Fu(n)21180 31315 y Fq(b)21638 31116 y Fr(i)22155 30633
y Fs(f)22567 31116 y Fx(\()p Fu(\257)74 b(;)221 b(q)48
b Fx(\))461 b(and)g Fr(h)p Fu(n)29905 31315 y Fq(b)30363
31116 y Fr(i)30880 30633 y Fs(w)31627 31116 y Fx(\()p
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b(ectiv)-36 b(e)461 b(left)4317 32721 y(and)528 b(righ)-36
b(t)527 b(deriv)-72 b(ativ)-36 b(es)529 b(of)f(the)g(free)g(energy)g
Fu(f)142 b Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))529
b(=)1001 b(lim)33373 33552 y Fq(V)210 b Fp(!)p Fi(L)35662
33675 y Fo(1)37583 32198 y Fs(1)p 36256 32415 3126 54
v 36256 33179 a Fp(j)p Fs(\244)37170 33302 y Fo(0)37631
33179 y Fs(\()p Fq(V)f Fs(\))p Fp(j)39735 32721 y Fx(ln)222
b Fu(Z)42026 32239 y Fs(b)26 b(c)43049 32721 y Fx(\()p
Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))4317
34841 y(with)434 b(resp)36 b(ect)433 b(to)h Fu(\257)74
b Fx(.)6268 36968 y(The)369 b(pro)36 b(of)369 b(of)h(di\256eren)-36
b(tiabilit)g(y)368 b(of)i Fu(f)142 b Fx(\()p Fu(\257)74
b(;)221 b(q)48 b Fx(\))368 b(for)h Fu(q)417 b Fx(=)368
b(2)h(and)g Fu(q)416 b Fr(\270)369 b Fx(4)g(ma)-36 b(y)369
b(b)36 b(e)369 b(found,)4317 38573 y(e.g.)579 b(in)434
b([B,)g(MM,)f(HKW)q(].)6268 40701 y(Let)350 b(us)g(also)h(men)-36
b(tion)349 b(that)h(for)h(the)f(p)36 b(ercolation)350
b(mo)36 b(del)351 b(\()p Fu(q)416 b Fx(=)369 b(1\))350
b(the)g(free)g(energy)4317 42306 y(is)391 b(ob)-36 b(viously)392
b(di\256eren)-36 b(tiable)390 b(for)i(an)-36 b(y)391
b(\(in)-36 b(v)g(erse\))390 b(temp)36 b(erature)390 b
Fu(\257)74 b Fx(.)564 b(Therefore)391 b(in)g(that)4317
43911 y(case)453 b Fu(\302)7904 43429 y Fs(f)8317 43911
y Fx(\()p Fu(\257)74 b(;)221 b(q)449 b Fx(=)401 b(1\))h(=)f
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b(;)221 b(q)449 b Fx(=)401 b(1\))h(=)f Fu(\302)25306
43429 y Fs(b)26 b(c)26328 43911 y Fx(\()p Fu(\257)74
b(;)221 b(q)449 b Fx(=)401 b(1\).)636 b(This)453 b(implies,)458
b(b)-36 b(y)452 b(Theorem)4317 45516 y(2,)462 b(that)455
b(at)h(the)f(transition)h(p)36 b(oin)-36 b(t)455 b Fu(\257)22611
45715 y Fq(t)23413 45516 y Fx(=)407 b(ln)221 b(2,)462
b(one)456 b(has)f Fu(\302)33173 45034 y Fs(b)26 b(c)34196
45516 y Fx(\()p Fu(\257)35436 45715 y Fq(t)35831 45516
y Fu(;)221 b(q)455 b Fx(=)406 b(1\))h(=)f(0)456 b(\(for)g(an)-36
b(y)4317 47121 y(b)36 b(c\).)4317 50083 y Fh(Theorem)499
b(4)651 b FA(Assume)413 b Fu(q)461 b FA(is)413 b(lar)-66
b(ge)413 b(enough,)423 b(then)412 b(the)h(me)-66 b(an)412
b(lo)-66 b(c)g(al)413 b(Euler)h(char)-66 b(acter-)4317
51688 y(istic)464 b(is)h(disc)-66 b(ontinuous)464 b(at)h
Fu(\257)18966 51887 y Fq(t)13688 54093 y Fu(\302)14503
53545 y Fs(f)14916 54093 y Fx(\()p Fu(\257)16156 54292
y Fq(t)16551 54093 y Fu(;)221 b(q)48 b Fx(\))369 b(=)f
Fr(\241)p Fu(\302)21861 53545 y Fs(w)22609 54093 y Fx(\()p
Fu(\257)23849 54292 y Fq(t)24245 54093 y Fu(;)221 b(q)48
b Fx(\))369 b(=)f(2)p Fu(q)28982 53545 y Fp(\241)p Fs(1)p
Fq(=)p Fs(2)31476 54093 y Fx(+)294 b Fu(O)36 b Fx(\()p
Fu(q)34943 53545 y Fp(\241)p Fs(7)p Fq(=)p Fs(12)37612
54093 y Fx(\))7058 b(\(21\))6268 57056 y Fh(Pro)42 b(of.)1016
b Fx(The)579 b(pro)36 b(of)581 b(is)e(mainly)i(based)e(on)g(a)h(con)-36
b(tour)579 b(represen)-36 b(tation)579 b(of)h(the)4317
58661 y(mo)36 b(del)425 b(deriv)-36 b(ed)423 b(in)h([LMMRS].)575
b(T)-108 b(o)425 b(de\257ne)e(these)g(con)-36 b(tours,)426
b(w)-36 b(e)424 b(\257rst)g(in)-36 b(tro)36 b(duce)423
b(the)4317 60266 y(co{b)36 b(oundary)494 b Fu(C)95 b
Fx(\()p Fu(X)104 b Fx(\))495 b(of)g(a)f(set)g(of)h(b)36
b(onds)494 b Fu(X)599 b Fx(as)494 b(the)g(set)g(of)g(b)36
b(onds)494 b(of)h Ft(L)41564 60465 y Fs(1)42425 60266
y Fr(n)337 b Fu(X)599 b Fx(that)4317 61871 y(con)-36
b(tain)434 b(1)f(or)h(t)-36 b(w)g(o)434 b(v)-36 b(ertices)434
b(in)g(\244\()p Fu(X)104 b Fx(\):)578 b Fu(C)95 b Fx(\()p
Fu(X)104 b Fx(\))370 b(=)e Fu(C)30197 62070 y Fs(1)30723
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62070 y Fs(2)35850 61871 y Fx(\()p Fu(X)104 b Fx(\))435
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66213 y Fu(C)12437 66412 y Fs(2)12962 66213 y Fx(\()p
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b(in)g(\244\()p Fu(X)104 b Fx(\))p Fr(g)25253 70015 y
Fx(10)p eop
%%Page: 11 11
11 10 bop 6268 7306 a Fx(A)567 b(subset)f Fu(\260)667
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b(oundary)567 b(of)g(a)g(set)g(of)4317 8911 y(b)36 b(onds)491
b Fu(X)597 b Fx(and)491 b(if)h(its)g(dual)g(is)g(a)g(connected)e(set)i
(of)g(b)36 b(onds.)752 b(The)492 b(connectedness)f(of)4317
10516 y(the)441 b(dual)h(of)h Fu(\260)514 b Fx(means)441
b(that)h(it)g(is)g(the)f(union)h(of)g(the)f(b)36 b(onds)442
b(of)g(a)g(sequence)g Fu(b)43534 10715 y Fs(1)44060 10516
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y Fq(i)p Fs(+1)27521 12121 y Fx(b)36 b(elongs)471 b(to)h(the)f(b)36
b(oundary)470 b(of)j(a)e(same)4317 13726 y(plaquette.)609
b(When)444 b Fu(X)549 b Fx(is)444 b(\257nite,)i Fu(\260)516
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(and)g Fu(X)548 b Fx(will)4317 15331 y(b)36 b(e)433 b(denoted)g(b)-36
b(y)434 b(In)-36 b(t)220 b Fu(\260)72 b Fx(.)579 b(The)433
b(length)h(of)g Fu(\260)505 b Fx(is)434 b(de\257ned)e(as)11288
18177 y Fr(k)p Fu(\260)72 b Fr(k)369 b Fx(=)g Fr(j)p
Fu(C)16413 18376 y Fs(1)16938 18177 y Fx(\()p Fu(X)104
b Fx(\))p Fr(j)296 b Fx(+)f Fr(j)p Fu(C)22405 18376 y
Fs(2)22930 18177 y Fx(\()p Fu(X)104 b Fx(\))p Fr(j)370
b Fx(=)e Fr(j)p Fu(C)28544 18376 y Fs(1)29070 18177 y
Fx(\(In)-36 b(t)220 b Fu(\260)72 b Fx(\))p Fr(j)295 b
Fx(+)g Fr(j)p Fu(C)35982 18376 y Fs(2)36507 18177 y Fx(\(In)-36
b(t)221 b Fu(\260)72 b Fx(\))p Fr(j)6268 21607 y Fx(As)434
b(a)g(result)f(of)h([LMMRS],)g(one)f(has)15130 24452
y Fu(Z)16115 23904 y Fs(f)16528 24452 y Fx(\()p Fu(V)72
b(;)221 b(\257)19180 24651 y Fq(t)19576 24452 y Fu(;)g(q)48
b Fx(\))369 b(=)g Fu(q)23664 23904 y Fp(j)p Fs(\244)24578
24027 y Fo(0)25038 23904 y Fs(\()p Fq(V)209 b Fs(\))p
Fp(j)p Fs(+)p Fp(j)p Fq(\270)p Fs(\()p Fq(V)h Fs(\))p
Fp(j)30136 24452 y Fr(Z)106 b Fx(\()p Fu(V)289 b Fr(j)p
Fu(')p Fx(\))16941 27551 y Fr(Z)106 b Fx(\()p Fu(V)288
b Fr(j)p Fu(')p Fx(\))369 b(=)26371 26289 y Fj(X)23039
29167 y Fp(f)p Fq(\260)23994 29290 y Fo(1)24455 29167
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25891 y Fq(n)31843 26289 y Fj(Y)31931 29089 y Fq(i)p
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Fr(j)368 b(\267)794 b Fu(cte)423 b Fr(j)p Fu(B)67 b Fx(\()p
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35079 y Fu(')p Fx(\()p Fu(\260)72 b Fx(\))433 b(of)i(con)-36
b(tours)433 b(are)g(giv)-36 b(en)435 b(b)-36 b(y)18670
38256 y Fu(')p Fx(\()p Fu(\260)72 b Fx(\))369 b(=)f Fu(q)23655
37707 y Fp(\241)24520 37260 y Fm(k)p Fn(\260)43 b Fm(k)p
24519 37506 1325 40 v 24979 38055 a Fo(4)25977 37707
y Fs(+)p Fq(\274)27281 37395 y Fo(0)27742 37707 y Fs(\(In)-26
b(t)156 b Fq(\260)52 b Fs(\))30424 38256 y Fu(e)31027
37707 y Fs(\242\()p Fq(\260)g Fs(\))45176 38256 y Fx(\(23\))4317
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43574 y Fp(\241)28203 43212 y Fo(1)p 28000 43373 812
40 v 28000 43921 a(12)29221 44123 y Fr(k)q Fu(\260)72
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b Fp(!)p Fi(L)37484 47290 y Fo(1)39683 46445 y Fs(1)p
38356 46662 3126 54 v 38356 47426 a Fp(j)p Fs(\244)39270
47549 y Fo(0)39731 47426 y Fs(\()p Fq(V)g Fs(\))p Fp(j)41835
46968 y Fx(ln)221 b Fr(Z)106 b Fx(\()p Fu(V)289 b Fr(j)p
Fu(')p Fx(\))4317 49038 y(of)565 b(the)f(con)-36 b(tour)563
b(mo)36 b(del)565 b(b)36 b(eha)-36 b(v)g(es)564 b(lik)-36
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y Fo(1)p 26794 48347 406 40 v 26794 48895 a(2)27772 49038
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b(w)564 b(that)g(the)4317 50643 y(dominan)-36 b(t)562
b(con)-36 b(tribution)561 b(to)h(the)g(lo)36 b(cal)564
b(Euler)e(c)-36 b(haracteristic)562 b Fu(\302)37635 50161
y Fs(f)38048 50643 y Fx(\()p Fu(\257)74 b(;)221 b(q)48
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b(b)36 b(e)526 b(seen)g(as)g(follo)-36 b(ws.)858 b(In)526
b(the)g(limit)g Fu(q)574 b Fr(!)527 b(1)p Fx(,)4317 53854
y(there)539 b(are)h(only)g(t)-36 b(w)g(o)540 b(ground)f(state)h
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55459 y(all)456 b(empt)-36 b(y)454 b(or)h(all)h(o)36
b(ccupied.)641 b(The)455 b(Euler)f(c)-36 b(haracteristic)455
b(of)h(suc)-36 b(h)454 b(con\257gurations)g(is)4317 57064
y(0.)853 b(The)525 b(\257rst)g(excitations)h(of)f(the)g(empt)-36
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58669 y(o)36 b(ccupied)362 b(b)36 b(onds)362 b(in)g(the)f(\\sea")j(of)f
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b(to)f Fu(\274)9410 59792 y Fs(0)10391 60274 y Fx(and)g(the)g(n)-36
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61879 y(the)481 b(Euler)h(c)-36 b(haracteristic)482 b(b)36
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61389 y Fp(\241)28156 61027 y Fo(1)p 28155 61188 V 28155
61736 a(2)28749 61879 y Fx(\).)723 b(Ho)-36 b(w)g(ev)g(er,)495
b(in)482 b(order)f(to)h(compute)4317 63484 y(the)k(co)36
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b(to)h(consider)g(the)f(expression)g(of)i(the)e(Euler)4317
65089 y(c)-36 b(haracteristic)350 b(in)g(terms)f(of)h(the)f(co)36
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65089 y Fx(and)f(more)h(precisely)g(the)f(expression)4317
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%%Page: 12 12
12 11 bop 6268 7306 a Fx(Notice)631 b(that)f Fu(\302)14377
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36 b(et)-36 b(w)g(een)479 b(2)g(v)-36 b(ertices)480 b
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Fp(2)p Fq(S)28215 12121 y Fu(d)p Fx(\()p Fu(x;)221 b(z)59
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b Fx(.)6268 15833 y(T)-108 b(o)434 b(compute)f Fr(h)p
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b(ev)-36 b(en)g(ts)5272 18096 y Fu(E)6235 18295 y Fq(f)7209
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b Fr(2)g(f)p Fx(0)p Fu(;)221 b Fx(1)p Fr(g)14974 17547
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b(of)g(the)f(origin)i(0)16740 20149 y(are)f(empt)-36
b(y)22448 19073 y Fj(\252)45176 20149 y Fx(\(25\))5587
22227 y Fu(E)446 b Fx(=)8377 21151 y Fj(\251)9152 22227
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b(oundary)434 b(of)g(sites)g(at)g(distance)f(1)h(from)16740
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33204 y Fq(f)24026 33005 y Fx(,)439 b Fu(\302)25641 33204
y Fs(0)26166 33005 y Fx(\()p Fu(n)p Fx(\))375 b(=)f(0)438
b(and)e(an)-36 b(y)437 b(con\257guration)g Fu(n)375 b
Fr(2)g Fu(E)78 b Fx(,)4317 34610 y Fu(\302)5132 34809
y Fs(0)5658 34610 y Fx(\()p Fu(n)p Fx(\))369 b(=)9328
34087 y Fs(1)p 9328 34305 471 54 v 9328 35069 a(2)9932
34610 y Fx(,)433 b(one)h(gets)13053 37591 y Fr(h)p Fu(\302)14385
37790 y Fs(0)14910 37591 y Fr(i)15427 36946 y Fs(f)16061
37591 y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48
b Fx(\))370 b(=)22383 36693 y(1)p 22383 37286 651 54
v 22383 38503 a(2)23388 37591 y(Pr\()p Fu(E)78 b Fx(\))294
b(+)29008 36329 y Fj(X)28433 39164 y Fq(n)p Fs(:)p Fq(n)p
Fp(2)p Fq(E)31203 38912 y Fm(0)31501 37591 y Fx([)p Fu(\302)32677
37790 y Fs(0)33203 37591 y Fx(\()p Fu(n)p Fx(\)])221
b(Pr\()p Fu(n)p Fx(\))6424 b(\(28\))4317 41215 y(It)330
b(is)f(easy)i(to)f(c)-36 b(hec)g(k)329 b(that)g(all)h(con\257guration)g
Fu(n)369 b Fr(2)g Fu(E)30099 40733 y Fp(0)30738 41215
y Fx(satisfy)331 b Fr(j)p Fu(\302)35879 41414 y Fq(x)36464
41215 y Fx(\()p Fu(n)p Fx(\))p Fr(j)369 b(\267)40525
40692 y Fs(1)p 40525 40910 471 54 v 40525 41673 a(2)41128
41215 y Fx(.)544 b(Therefore)17102 44766 y(2)17973 42441
y Fj(\257)17973 43238 y(\257)17973 44035 y(\257)17973
44832 y(\257)17973 45629 y(\257)18991 43504 y(X)18417
46339 y Fq(n)p Fs(:)p Fq(n)p Fp(2)p Fq(E)21187 46087
y Fm(0)21485 44766 y Fx([)p Fu(\302)22661 44965 y Fs(0)23187
44766 y Fx(\()p Fu(n)p Fx(\)])221 b(Pr\()p Fu(n)p Fx(\))28736
42441 y Fj(\257)28736 43238 y(\257)28736 44035 y(\257)28736
44832 y(\257)28736 45629 y(\257)29548 44766 y Fr(\267)369
b Fx(Pr\()p Fu(E)33888 44217 y Fp(0)34198 44766 y Fx(\))10472
b(\(29\))4317 48218 y(whic)-36 b(h)433 b(is)h(b)36 b(ounded)432
b(b)-36 b(y)15840 50481 y(Pr\()p Fu(E)18778 49932 y Fp(0)19088
50481 y Fx(\))369 b Fr(\267)g Fx(Pr\()p Fr(9)p Fu(\260)440
b Fx(:)370 b Fu(\260)441 b Fr(3)368 b Fx(0;)221 b Fr(j)g
Fx(In)-36 b(t)222 b Fu(\260)72 b Fr(j)369 b(\270)g Fx(2\))9211
b(\(30\))4317 52743 y(Actually)-108 b(,)515 b(for)499
b(ev)-36 b(ery)498 b(con\257guration)g Fu(n)479 b Fr(2)g
Fu(E)27075 52261 y Fp(0)27385 52743 y Fx(,)514 b(there)498
b(exists)g(a)h(con)-36 b(tour)497 b Fu(\260)551 b Fr(3)478
b Fx(0)498 b(suc)-36 b(h)4317 54349 y(that)514 b Fr(j)221
b Fx(In)-36 b(t)221 b Fu(\260)72 b Fr(j)506 b(\270)g
Fx(2.)821 b(T)-108 b(aking)515 b(in)-36 b(to)514 b(accoun)-36
b(t)514 b(that)f(the)h(minimal)g(length)g(of)h(con)-36
b(tours)4317 55954 y(with)584 b Fr(j)221 b Fx(In)-36
b(t)222 b Fu(\260)72 b Fr(j)625 b(\270)g Fx(2)585 b(is)f(8)h(and)e
(that)h Fu(\274)23665 55472 y Fs(0)24190 55954 y Fx(\(In)-36
b(t)221 b Fu(\260)72 b Fx(\))625 b Fr(\267)30248 55431
y Fs(1)p 30248 55648 V 30248 56412 a(6)31073 55954 y
Fr(k)p Fu(\260)72 b Fr(k)p Fx(,)622 b(this)584 b(probabilit)-36
b(y)585 b(can)f(b)36 b(e)4317 57559 y(estimated)434 b(b)-36
b(y)433 b(P)-36 b(eierls)434 b(t)-36 b(yp)36 b(e)434
b(argumen)-36 b(ts)432 b(as)i(follo)-36 b(ws)7057 59980
y(Pr\()p Fu(E)9995 59431 y Fp(0)10305 59980 y Fx(\))369
b Fr(\267)14858 58718 y Fj(X)12582 61596 y Fq(\260)52
b Fs(:)p Fq(\260)g Fp(3)p Fs(0;)p Fp(j)158 b Fs(In)-26
b(t)157 b Fq(\260)52 b Fp(j\270)p Fs(2)19275 59980 y
Fx(Pr)o(\()p Fu(\260)72 b Fx(\))369 b Fr(\267)25923 58718
y Fj(X)24195 61596 y Fq(\260)52 b Fs(:)p Fq(\260)g Fp(3)p
Fs(0;)p Fp(k)r Fq(\260)g Fp(k\270)p Fs(8)29791 59980
y Fu(')p Fx(\()p Fu(\260)72 b Fx(\))11180 64868 y Fr(\267)12640
63606 y Fj(X)12582 66412 y Fq(m)p Fp(\270)p Fs(8)14838
64868 y Fu(m)15976 64320 y Fs(2)16501 64868 y Fx(4)17151
64320 y Fq(m)18039 63792 y Fj(\241)18648 64868 y Fu(q)19273
64320 y Fp(\241)20138 63958 y Fo(1)p 20137 64119 406
40 v 20137 64667 a(4)20731 64868 y Fu(e)21334 64320 y
Fs(6)p Fq(q)22256 63914 y Fm(\241)23232 63653 y Fo(1)p
23029 63764 812 33 v 23029 64224 a(12)24084 63792 y Fj(\242)24693
64090 y Fq(m)25950 64868 y Fr(\267)369 b Fx(2)295 b Fr(\242)g
Fx(8)29611 64320 y Fs(2)30433 64868 y Fr(\242)g Fx(4)31747
64320 y Fs(8)34401 63969 y Fu(q)35026 63479 y Fp(\241)35891
63117 y Fo(3)p 35890 63278 406 40 v 35890 63826 a(4)36485
63969 y Fu(e)37088 63487 y Fs(48)p Fq(q)38480 63082 y
Fm(\241)39456 62821 y Fo(1)p 39253 62932 812 33 v 39253
63392 a(12)p 32406 64563 9898 54 v 32406 66200 a Fx(\(1)g
Fr(\241)h Fx(4)p Fu(q)36461 65710 y Fp(\241)37326 65348
y Fo(1)p 37325 65509 406 40 v 37325 66057 a(4)37919 66200
y Fu(e)38522 65816 y Fs(6)p Fq(q)39444 65411 y Fm(\241)40419
65150 y Fo(1)p 40217 65261 812 33 v 40217 65721 a(12)41272
66200 y Fx(\))41778 65816 y Fs(3)45176 64868 y Fx(\(31\))25253
70015 y(12)p eop
%%Page: 13 13
13 12 bop 4317 7554 a Fx(pro)-36 b(vided)516 b Fu(q)10372
7064 y Fp(\241)11237 6702 y Fo(1)p 11236 6863 406 40
v 11236 7411 a(4)11830 7554 y Fu(e)12433 7072 y Fs(6)p
Fq(q)13355 6666 y Fm(\241)14330 6406 y Fo(1)p 14127 6517
812 33 v 14127 6977 a(12)15692 7554 y Fu(<)17346 7031
y Fs(1)p 17346 7248 471 54 v 17346 8012 a(4)17949 7554
y Fx(.)826 b(Here)516 b(w)-36 b(e)517 b(used)e(the)h(equalit)-36
b(y)517 b(\(23\))f(and)g(the)f(fact)i(that)4317 9159
y(the)494 b(n)-36 b(um)g(b)36 b(er)493 b(of)i(con)-36
b(tours)494 b(of)i(length)e Fu(m)g Fx(that)g(con)-36
b(tain)494 b(a)h(giv)-36 b(en)495 b(p)36 b(oin)-36 b(t)494
b(is)h(less)g(than)4317 10764 y Fu(m)5455 10282 y Fs(2)5981
10764 y Fx(4)6631 10282 y Fq(m)7519 10764 y Fx(.)6268
12967 y(On)d(the)g(other)h(hand,)507 b(in)493 b(order)f(to)h(estimate)g
(the)g(probabilit)-36 b(y)493 b(Pr)o(\()p Fu(E)78 b Fx(\))493
b(w)-36 b(e)493 b(let)541 b(\271)-698 b Fu(\260)4317
14572 y Fx(to)548 b(b)36 b(e)548 b(the)f(set)h(constituted)f(b)-36
b(y)547 b(the)g(six)i(b)36 b(onds)547 b(con)-36 b(taining)548
b(one)g(endp)36 b(oin)-36 b(t)547 b(of)h(the)4317 16177
y(o)36 b(ccupied)433 b(b)36 b(ond)433 b(as)h(endp)36
b(oin)-36 b(t)433 b(but)f(not)h(b)36 b(oth)433 b(of)i(them.)578
b(Then)7389 22537 y(Pr\()p Fu(E)78 b Fx(\))368 b(=)h(4)15162
18787 y Fj(X)13365 21665 y Fp(f)p Fq(\260)14320 21788
y Fo(1)14781 21665 y Fq(;:::;\260)16571 21776 y Fn(n)17139
21665 y Fp(g)q(\276)33 b Fs(\271)-503 b Fq(\260)19663
18389 y(n)19100 18787 y Fj(Y)19187 21586 y Fq(i)p Fs(=1)21019
20049 y Fu(')p Fx(\()p Fu(\260)23052 20248 y Fq(i)23427
20049 y Fx(\))p 13365 22232 10568 54 v 16475 23449 a
Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p Fu(')p Fx(\))24434
22537 y(=)369 b(4)p Fu(')p Fx(\()48 b(\271)-698 b Fu(\260)72
b Fx(\))32104 18787 y Fj(X)29209 21665 y Fp(f)p Fq(\260)30164
21788 y Fo(1)30625 21665 y Fq(;:::;\260)32415 21776 y
Fn(n)32983 21665 y Fp(g)q Fq(;\260)34200 21800 y Fn(i)34551
21665 y Fp(\\)33 b Fs(\271)-503 b Fq(\260)52 b Fs(=)p
Fp(;)37702 18389 y Fq(n)37139 18787 y Fj(Y)37226 21586
y Fq(i)p Fs(=1)39057 20049 y Fu(')p Fx(\()p Fu(\260)41090
20248 y Fq(i)41466 20049 y Fx(\))p 29209 22232 12763
54 v 33416 23449 a Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p
Fu(')p Fx(\))45176 22537 y(\(32\))4317 26142 y(The)429
b(factor)h(4)g(stems)f(from)h(the)e(fact)i(that)f(there)f(are)i(4)f(b)
36 b(onds)429 b(in)g(the)f(co{b)36 b(oundary)4317 27747
y(of)434 b(0:)579 b(w)-36 b(e)434 b(tak)-36 b(e)434 b
Fu(V)723 b Fx(to)434 b(b)36 b(e)433 b(a)h(b)36 b(o)-36
b(x)434 b(cen)-36 b(tered)432 b(at)i(the)f(origin.)6268
29950 y(The)540 b(last)g(ratio)g(can)g(b)36 b(e)540 b(estimated)f(b)-36
b(y)540 b(cluster)f(expansion)h([D)q(,)g(M].)897 b(F)-108
b(or)539 b(that)4317 31555 y(purp)36 b(ose)408 b(w)-36
b(e)409 b(in)-36 b(tro)36 b(duce)408 b(clusters)g Fu(X)514
b Fx(as)409 b(m)-36 b(ulti-indexes)408 b(de\257ned)f(on)i(the)f(sets)h
(of)g(con-)4317 33160 y(tours)494 b(with)h(in)-36 b(teger)495
b(v)-72 b(alues.)762 b(The)494 b(supp)36 b(ort)494 b(Supp)220
b Fu(X)599 b Fx(of)495 b(a)g(cluster)g Fu(X)599 b Fx(is)495
b(the)f(set)h(of)4317 34765 y(con)-36 b(tours)368 b Fu(\260)440
b Fx(for)369 b(whic)-36 b(h)369 b Fu(X)104 b Fx(\()p
Fu(\260)72 b Fx(\))369 b Fr(\270)g Fx(1.)557 b(W)-108
b(e)369 b(also)g(in)-36 b(tro)36 b(duce)368 b(the)g(truncated)f
(functionals:)16757 38432 y Fu(\301)17527 37883 y Fq(T)18261
38432 y Fx(\()p Fu(X)104 b Fx(\))369 b(=)23511 37533
y Fu(a)p Fx(\()p Fu(X)104 b Fx(\))p 22339 38126 5223
54 v 22339 38418 a Fj(Y)22919 41208 y Fq(\260)24257 39680
y Fu(X)g Fx(\()p Fu(\260)72 b Fx(\)!)27915 37170 y Fj(Y)28496
39959 y Fq(\260)29834 38432 y Fu(')p Fx(\()p Fu(X)104
b Fx(\))32881 37883 y Fq(X)69 b Fs(\()p Fq(\260)52 b
Fs(\))45176 38432 y Fx(\(33\))4317 43948 y(The)560 b(co)36
b(e\261cien)-36 b(t)559 b Fu(a)p Fx(\()p Fu(X)104 b Fx(\))560
b(is)g(a)g(com)-36 b(binatoric)560 b(factor)g(de\257ned)e(in)i(terms)f
(of)h(the)f(con-)4317 45553 y(nectivit)-36 b(y)520 b(prop)36
b(erties)519 b(of)h(the)f(graph)f Fu(G)p Fx(\()p Fu(X)104
b Fx(\))520 b(with)f(v)-36 b(ertices)520 b(corresp)36
b(onding)519 b(to)g Fu(\260)587 b Fr(2)4317 47158 y Fx(Supp)220
b Fu(X)605 b Fx(\(there)500 b(are)h Fu(X)104 b Fx(\()p
Fu(\260)72 b Fx(\))501 b(v)-36 b(ertices)501 b(for)g(eac)-36
b(h)501 b Fu(\260)555 b Fr(2)482 b Fx(Supp)220 b Fu(X)104
b Fx(\))501 b(b)36 b(eing)501 b(connected)f(b)-36 b(y)4317
48763 y(an)434 b(edge)f(whenev)-36 b(er)434 b(the)f(corresp)36
b(onding)433 b(con)-36 b(tours)433 b(are)h(not)f(compatible.)6268
50966 y(As)h(a)g(result)f(w)-36 b(e)434 b(ha)-36 b(v)g(e)18190
52786 y Fj(X)15936 55664 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69
b Fp(\\)p Fq(b)p Fp(6)p Fs(=)p Fp(;)22585 54048 y Fr(j)p
Fu(\301)23724 53500 y Fq(T)24457 54048 y Fx(\()p Fu(X)104
b Fx(\))p Fr(j)370 b(\267)f Fx(\()p Fu(q)29924 53500
y Fp(\241)30789 53138 y Fo(1)p 30788 53299 406 40 v 30788
53847 a(4)31382 54048 y Fu(e)31985 53500 y Fs(6)p Fq(q)32907
53094 y Fm(\241)33882 52833 y Fo(1)p 33680 52944 812
33 v 33680 53404 a(12)34735 52972 y Fj(\242)35344 53269
y Fs(6)45176 54048 y Fx(\(34\))4317 58985 y(for)380 b(4)p
Fu(g)48 b(q)8196 58494 y Fp(\241)9061 58132 y Fo(1)p
9060 58293 406 40 v 9060 58842 a(4)9654 58985 y Fu(e)10257
58503 y Fs(6)p Fq(q)11179 58097 y Fm(\241)12154 57836
y Fo(1)p 11952 57947 812 33 v 11952 58407 a(12)13376
58985 y Fu(<)368 b Fx(1,)391 b(where)380 b Fu(g)416 b
Fr(\274)369 b Fu(e)22906 58503 y Fs(1)p Fq(:)p Fs(58)25013
58985 y Fx([KP)q(,)380 b(M)o(].)561 b(This)380 b(is)f(actually)i(a)f
(consequence)4317 61004 y(of)495 b(the)f(theorem)g(giv)-36
b(en)496 b(in)e([M])h(using)f(that)g Fu(')p Fx(\()p Fu(\260)72
b Fx(\))472 b(=)h(\()p Fu(q)32766 60513 y Fp(\241)33631
60151 y Fo(1)p 33630 60312 406 40 v 33630 60861 a(4)34224
61004 y Fu(e)34827 60522 y Fs(6)p Fq(q)35749 60116 y
Fm(\241)36724 59855 y Fo(1)p 36521 59966 812 33 v 36521
60426 a(12)37577 59928 y Fj(\242)38185 60225 y Fp(k)q
Fq(\260)52 b Fp(k)40213 61004 y Fx(and)494 b(that)g(the)4317
62609 y(minimal)434 b(length)g(of)g(con)-36 b(tours)433
b(is)h(6.)25253 70015 y(13)p eop
%%Page: 14 14
14 13 bop 6268 7306 a Fx(Moreo)-36 b(v)g(er)310 b(b)36
b(oth)308 b(terms)h(in)g(the)g(ratio)g(of)h(the)f(r.h.s.)537
b(of)310 b(\(32\))f(can)g(b)36 b(e)309 b(exp)36 b(onen)-36
b(tiated)4317 8911 y(in)434 b(terms)f(of)h(the)f(truncated)f
(functionals)i(leading)g(to)9415 12746 y(Pr)o(\()p Fu(E)78
b Fx(\))369 b(=)f(4)p Fu(')p Fx(\()48 b(\271)-698 b Fu(\260)72
b Fx(\))221 b(exp)20298 10023 y Fj(8)20298 11218 y(<)20298
13609 y(:)23800 11484 y(X)21479 14362 y Fq(X)69 b Fs(:Supp)156
b Fq(X)69 b Fp(\\)33 b Fs(\271)-503 b Fq(\260)52 b Fs(=)p
Fp(;)28262 12746 y Fu(\301)29032 12198 y Fq(T)29765 12746
y Fx(\()p Fu(X)104 b Fx(\))296 b Fr(\241)33585 11484
y Fj(X)34122 14303 y Fq(X)35725 12746 y Fu(\301)36495
12198 y Fq(T)37228 12746 y Fx(\()p Fu(X)104 b Fx(\))39423
10023 y Fj(9)39423 11218 y(=)39423 13609 y(;)13227 17971
y Fx(=)368 b(4)p Fu(')p Fx(\()48 b(\271)-698 b Fu(\260)72
b Fx(\))221 b(exp)20298 15248 y Fj(8)20298 16443 y(<)20298
18834 y(:)21479 17971 y Fr(\241)25055 16709 y Fj(X)22733
19587 y Fq(X)69 b Fs(:Supp)157 b Fq(X)69 b Fp(\\)33 b
Fs(\271)-503 b Fq(\260)52 b Fp(6)p Fs(=)p Fp(;)29516
17971 y Fu(\301)30286 17422 y Fq(T)31020 17971 y Fx(\()p
Fu(X)104 b Fx(\))33215 15248 y Fj(9)33215 16443 y(=)33215
18834 y(;)13227 23196 y Fx(=)368 b(4)p Fu(q)15882 22647
y Fp(\241)16747 22200 y Fm(k)35 b Fo(\271)-441 b Fn(\260)43
b Fm(k)p 16747 22446 1325 40 v 17206 22995 a Fo(4)18204
22647 y Fs(+)p Fq(\274)19508 22335 y Fo(0)19969 22647
y Fs(\(In)-26 b(t)190 b(\271)-504 b Fq(\260)52 b Fs(\))22873
23196 y Fx(exp)25082 20473 y Fj(8)25082 21668 y(<)25082
24059 y(:)26262 23196 y Fx(\242\()c(\271)-698 b Fu(\260)72
b Fx(\))295 b Fr(\241)33050 21934 y Fj(X)30728 24812
y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp(\\)33 b Fs(\271)-503
b Fq(\260)53 b Fp(6)p Fs(=)p Fp(;)37511 23196 y Fu(\301)38281
22647 y Fq(T)39015 23196 y Fx(\()p Fu(X)104 b Fx(\))41210
20473 y Fj(9)41210 21668 y(=)41210 24059 y(;)13227 28421
y Fx(=)368 b(4)p Fu(q)15882 27872 y Fp(\241)16747 27510
y Fo(1)p 16747 27671 406 40 v 16747 28220 a(2)17562 28421
y Fx(exp)19771 25698 y Fj(8)19771 26893 y(<)19771 29284
y(:)20951 28421 y Fx(\242\()48 b(\271)-698 b Fu(\260)72
b Fx(\))295 b Fr(\241)27739 27159 y Fj(X)25417 30037
y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp(\\)33 b Fs(\271)-503
b Fq(\260)53 b Fp(6)p Fs(=)p Fp(;)32200 28421 y Fu(\301)32970
27872 y Fq(T)33704 28421 y Fx(\()p Fu(X)104 b Fx(\))35899
25698 y Fj(9)35899 26893 y(=)35899 29284 y(;)45176 28421
y Fx(\(35\))4317 32330 y(F)-108 b(or)503 b(the)g(last)g(t)-36
b(w)g(o)504 b(equalities,)522 b(w)-36 b(e)503 b(ha)-36
b(v)g(e)504 b(tak)-36 b(en)503 b(in)-36 b(to)503 b(accoun)-36
b(t)503 b(the)g(expression)g(\(23\))4317 33935 y(and)467
b(the)f(fact)i(that)f Fr(k)48 b Fx(\271)-698 b Fu(\260)72
b Fr(k)426 b Fx(=)g(6)468 b(and)e Fu(\274)23009 33453
y Fs(0)23535 33935 y Fx(\(In)-36 b(t)269 b(\271)-699
b Fu(\260)72 b Fx(\))426 b(=)g(1.)679 b(According)468
b(to)f(\(34\))g(the)g(sum)g(in)4317 35540 y(the)433 b(exp)36
b(onen)-36 b(tial)434 b(satis\257es)12721 36652 y Fj(\257)12721
37449 y(\257)12721 38246 y(\257)12721 39043 y(\257)12721
39840 y(\257)12721 40637 y(\257)15485 38113 y(X)13163
40991 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp(\\)33 b
Fs(\271)-503 b Fq(\260)53 b Fp(6)p Fs(=)p Fp(;)19946
39375 y Fu(\301)20716 38826 y Fq(T)21450 39375 y Fx(\()p
Fu(X)104 b Fx(\))23645 36652 y Fj(\257)23645 37449 y(\257)23645
38246 y(\257)23645 39043 y(\257)23645 39840 y(\257)23645
40637 y(\257)24457 39375 y Fr(\267)25859 38113 y Fj(X)26035
40942 y Fq(b)p Fp(2)33 b Fs(\271)-503 b Fq(\260)30254
38113 y Fj(X)27999 40991 y Fq(X)69 b Fs(:Supp)157 b Fq(X)69
b Fp(\\)p Fq(b)p Fp(6)p Fs(=)p Fp(;)34648 39375 y Fr(j)p
Fu(\301)35787 38826 y Fq(T)36521 39375 y Fx(\()p Fu(X)104
b Fx(\))p Fr(j)24457 43519 y(\267)369 b(k)49 b Fx(\271)-698
b Fu(\260)71 b Fr(k)222 b Fx(\(4)p Fu(g)48 b Fx(\))30489
42971 y Fs(6)31014 43519 y Fu(q)31639 42971 y Fp(\241)32504
42609 y Fo(3)p 32503 42770 V 32503 43318 a(2)33097 43519
y Fu(e)33700 42971 y Fs(36)p Fq(q)35092 42565 y Fm(\241)36068
42305 y Fo(1)p 35865 42416 812 33 v 35865 42875 a(12)45176
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%%Page: 15 15
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%%Page: 16 16
16 15 bop 4317 7306 a Fx(where)434 b Fu(\274)8861 6824
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%%Page: 17 17
17 16 bop 4317 7306 a Fh(Theorem)499 b(5)1301 b FA(a\))466
b(The)e(fol)66 b(lowing)465 b(limits)f(exist)g(and)h(c)-66
b(oincide)11639 11191 y Fx(lim)11168 12023 y Fq(V)209
b Fp(!)p Fi(L)13456 12146 y Fo(1)14138 9318 y Fj(\277)16930
10293 y Fu(\302)-786 b(\302)g(\302)g(\302)p 15268 10886
4226 54 v 15268 12103 a Fr(j)p Fx(\244)16540 12302 y
Fs(0)17065 12103 y Fx(\()p Fu(V)289 b Fx(\))p Fr(j)19626
9318 y Fj(\300)20622 9616 y Fs(f)21256 11191 y Fx(\()p
Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))370
b(=)840 b(lim)27446 12023 y Fq(V)209 b Fp(!)p Fi(L)29734
12146 y Fo(1)30417 11191 y Fr(h)o Fu(\302)31748 11390
y Fs(0)32274 11191 y Fr(i)32791 10546 y Fs(f)33425 11191
y Fx(\()p Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48 b
Fx(\))369 b Fr(\264)h Fu(\302)40451 10643 y Fs(f)40863
11191 y Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))1937
b(\(7\))7569 14739 y FA(and)485 b(de\257ne)f(the)g(me)-66
b(an)484 b(lo)-66 b(c)g(al)485 b(Euler)g(char)-66 b(acteristic)483
b(with)i(fr)-66 b(e)g(e)483 b(b)-66 b(oundary)485 b(c)-66
b(on-)7569 16344 y(dition)463 b Fu(\302)12136 15862 y
Fs(f)12549 16344 y Fx(\()p Fu(\257)74 b(;)221 b(q)48
b Fx(\))p FA(.)4967 19034 y(b\))466 b(A)-33 b(nalo)-66
b(gously,)464 b(the)g(fol)66 b(lowing)465 b(limits)f(exist)g(and)h(c)
-66 b(oincide)10305 22686 y Fx(lim)9834 23517 y Fq(V)209
b Fp(!)p Fi(L)12122 23640 y Fo(1)12805 20813 y Fj(\277)15596
21787 y Fu(\302)-786 b(\302)g(\302)g(\302)p 13934 22380
V 13934 23597 a Fr(j)p Fx(\244)15206 23796 y Fs(0)15731
23597 y Fx(\()p Fu(V)290 b Fx(\))p Fr(j)18292 20813 y
Fj(\300)19288 21110 y Fs(w)20258 22686 y Fx(\()p Fu(V)72
b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))370 b(=)840
b(lim)26447 23517 y Fq(V)209 b Fp(!)p Fi(L)28735 23640
y Fo(1)29418 22686 y Fr(h)p Fu(\302)30750 22885 y Fs(0)31275
22686 y Fr(i)31792 22040 y Fs(w)32761 22686 y Fx(\()p
Fu(V)72 b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))370
b Fr(\264)f Fu(\302)39787 22138 y Fs(w)40535 22686 y
Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))2265 b(\(8\))7569
26233 y FA(and)392 b(de\257ne)f(the)g(me)-66 b(an)391
b(lo)-66 b(c)g(al)392 b(Euler)g(char)-66 b(acteristic)390
b(with)i(wir)-66 b(e)g(d)391 b(b)-66 b(oundary)392 b(c)-66
b(on-)7569 27838 y(dition)463 b Fu(\302)12136 27356 y
Fs(w)12884 27838 y Fx(\()p Fu(\257)74 b(;)221 b(q)48
b Fx(\))p FA(.)6268 31382 y Fx(It)355 b(is)g(kno)-36
b(wn)355 b(that,)370 b(for)356 b(large)f Fu(q)402 b Fx(and)354
b Fu(d)369 b Fr(\270)g Fx(2,)j(the)354 b(mo)36 b(del)355
b(exhibits)g(a)g(\(temp)36 b(erature)4317 32987 y(driv)-36
b(en\))395 b(\257rst)g(order)h(phase)f(transition)h(at)g(some)g(in)-36
b(v)g(erse)396 b(temp)36 b(erature)395 b Fu(\257)41383
33186 y Fq(t)42174 32987 y Fx(\()p Fr(\274)44222 32464
y Fs(1)p 44215 32682 485 54 v 44215 33446 a Fq(d)45053
32987 y Fx(ln)221 b Fu(q)48 b Fx(\))4317 34593 y(where)443
b(the)g(mean)g(energy)18397 34070 y Fq(d)p 18110 34287
1058 54 v 18110 35051 a(d\257)19300 34593 y Fu(f)142
b Fx(\()p Fu(\257)74 b(;)221 b(q)48 b Fx(\))443 b(is)h(discon)-36
b(tin)g(uous)442 b([KS].)608 b(The)444 b(follo)-36 b(wing)445
b(theo-)4317 36198 y(rem)433 b(sho)-36 b(ws)434 b(that)f(it)h(is)g
(also)g(the)g(case)g(for)g(the)f(mean)g(lo)36 b(cal)435
b(Euler)e(c)-36 b(haracteristic.)4317 39742 y Fh(Theorem)499
b(6)651 b FA(Assume)546 b(that)f Fu(q)593 b FA(is)545
b(lar)-66 b(ge)545 b(enough,)565 b(then)545 b(ther)-66
b(e)544 b(exists)h(a)h(unique)f(in-)4317 41347 y(verse)435
b(temp)-66 b(er)g(atur)g(e)432 b Fu(\257)15435 41546
y Fq(t)16266 41347 y FA(wher)-66 b(e)434 b(the)h(me)-66
b(an)433 b(lo)-66 b(c)g(al)435 b(Euler)g(char)-66 b(acteristic)433
b(is)h(disc)-66 b(ontinu-)4317 42952 y(ous.)15554 45809
y Fu(\302)16369 45261 y Fs(f)16781 45809 y Fx(\()p Fu(\257)18021
46008 y Fq(t)18416 45809 y Fu(;)221 b(q)48 b Fx(\))369
b(=)g Fu(d)221 b(q)23401 45261 y Fp(\241)24266 44887
y Fn(d)p Fm(\241)p Fo(1)p 24265 45059 1473 40 v 24788
45608 a Fn(d)26221 45809 y Fx(+)294 b Fu(O)36 b Fx(\()p
Fu(q)29688 45227 y Fp(\241)30553 44853 y Fn(d)p Fm(\241)p
Fo(1)p 30552 45025 V 31075 45574 a Fn(d)32157 45227 y
Fs([1+)34490 44864 y Fo(1)p 33754 45025 1879 40 v 33754
45574 a(4)p Fn(d)p Fm(\241)p Fo(2)35765 45227 y Fs(])36082
45809 y Fx(\))9239 b(\(9\))15218 48072 y Fu(\302)16033
47523 y Fs(w)16781 48072 y Fx(\()p Fu(\257)18021 48271
y Fq(t)18416 48072 y Fu(;)221 b(q)48 b Fx(\))369 b(=)g(\()p
Fr(\241)p Fx(1\))24574 47523 y Fq(d)p Fp(\241)p Fs(1)26316
48072 y Fu(d)221 b(q)27838 47523 y Fp(\241)28713 47161
y Fo(1)p 28702 47322 427 40 v 28702 47871 a Fn(d)29612
48072 y Fx(+)295 b Fu(O)36 b Fx(\()p Fu(q)33080 47523
y Fp(\241)33955 47161 y Fo(1)p 33944 47322 V 33944 47871
a Fn(d)34503 47523 y Fp(\241)35368 47161 y Fo(1)p 35368
47322 406 40 v 35368 47871 a(2)35962 48072 y Fx(\))8708
b(\(10\))4317 50929 y FA(and)465 b(for)g(every)f Fu(\257)443
b Fr(6)p Fx(=)368 b Fu(\257)15645 51128 y Fq(t)20606
52534 y Fu(\302)21421 51986 y Fs(f)21834 52534 y Fx(\()p
Fu(\257)74 b(;)221 b(q)48 b Fx(\))368 b(=)h Fu(\302)27425
51986 y Fs(w)28173 52534 y Fx(\()p Fu(\257)74 b(;)221
b(q)48 b Fx(\))13976 b(\(11\))6268 56196 y(Note)502 b(that)g(while)g
(the)g(jump)f(of)h(the)g(mean)g(energy)g(is)g(\242)p
Fu(E)563 b Fx(=)485 b(1)342 b Fr(\241)g Fu(O)36 b Fx(\()p
Fu(q)43196 55706 y Fp(\241)44071 55344 y Fo(1)p 44060
55505 427 40 v 44060 56053 a Fn(d)44674 56196 y Fx(\))502
b(the)4317 57919 y(jump)476 b(\242)p Fu(\302)441 b Fx(=)g
Fr(j)p Fu(\302)12697 57437 y Fq(f)13302 57919 y Fx(\()p
Fu(\257)14542 58118 y Fq(t)14937 57919 y Fu(;)221 b(q)48
b Fx(\))324 b Fr(\241)h Fu(\302)19147 57437 y Fq(w)19901
57919 y Fx(\()p Fu(\257)21141 58118 y Fq(t)21536 57919
y Fu(;)221 b(q)48 b Fx(\))p Fr(j)442 b Fx(=)f Fu(O)36
b Fx(\()p Fu(q)27674 57429 y Fp(\241)28549 57067 y Fo(1)p
28538 57228 V 28538 57776 a Fn(d)29153 57919 y Fx(\))476
b(for)h(ev)-36 b(en)476 b(space)g(dimensions)g(and)4317
59687 y(\242)p Fu(\302)369 b Fx(=)f Fu(O)36 b Fx(\()p
Fu(q)10126 59197 y Fp(\241)10991 58823 y Fn(d)p Fm(\241)p
Fo(1)p 10990 58995 1473 40 v 11513 59544 a Fn(d)12651
59687 y Fx(\))433 b(for)h(o)36 b(dd)433 b(space)h(dimensions.)6268
61879 y Fh(Pro)42 b(of)507 b(of)h(Theorem)h(6.)1301 b
Fx(W)-108 b(e)441 b(b)36 b(egin)442 b(with)g(the)f(pro)36
b(of)443 b(of)f(\(9\))g(whic)-36 b(h)442 b(is)g(based,)4317
63484 y(as)379 b(in)e(Section)h(2,)390 b(on)378 b(a)g(con)-36
b(tour)378 b(represen)-36 b(tation)377 b(of)i(the)e(mo)36
b(del)379 b([LMMRS)o(].)560 b(W)-108 b(e)378 b(\257rst)4317
65089 y(in)-36 b(tro)36 b(duce)522 b(some)h(geometrical)h
(de\257nitions.)844 b(Tw)-36 b(o)524 b(b)36 b(onds)522
b(are)h(said)f(co{adjacen)-36 b(t)524 b(if)4317 66694
y(there)463 b(exists)i(a)f Fu(d)p Fx({cell)h(con)-36
b(taining)464 b(these)f(t)-36 b(w)g(o)465 b(b)36 b(onds.)668
b(A)464 b(set)g(of)g(b)36 b(onds,)471 b Fu(X)104 b Fx(,)473
b(is)464 b(said)25253 70015 y(17)p eop
%%Page: 18 18
18 17 bop 4317 7306 a Fx(co{connected)428 b(if)g(for)g(an)-36
b(y)428 b Fu(b)f Fx(and)g Fu(b)21934 6824 y Fp(0)22672
7306 y Fx(in)h Fu(X)104 b Fx(,)430 b(there)d(exists)h(a)g(sequence)f
(of)h(b)36 b(onds)427 b(in)h Fu(X)4317 8911 y(b)473 b
Fx(=)f Fu(b)7380 9110 y Fs(1)7906 8911 y Fu(;)221 b(:)g(:)g(:)j(;)d(b)
11372 9110 y Fq(n)12471 8911 y Fx(=)473 b Fu(b)14509
8429 y Fp(0)14819 8911 y Fx(,)510 b(suc)-36 b(h)494 b(that)g
Fu(b)22117 9110 y Fq(i)22987 8911 y Fx(and)g Fu(b)26130
9110 y Fq(i)p Fs(+1)28203 8911 y Fx(are)h(co{adjacen)-36
b(t.)762 b(W)-108 b(e)494 b(note)g(that)g(to)4317 10516
y(an)-36 b(y)457 b Fu(p)p Fx({cell)h(in)e Ft(L)h Fx(w)-36
b(e)457 b(can)f(asso)36 b(ciate)459 b(the)d(orthogonal)h(\()p
Fu(d)311 b Fr(\241)g Fu(p)p Fx(\){cell)458 b(of)f(the)f(dual)h(cell)
4317 12121 y(complex)439 b Ft(L)10302 11639 y Fp(\244)11266
12121 y Fx(corresp)36 b(onding)437 b(to)i(the)e(dual)h(lattice)h(\()p
Ft(Z)298 b Fx(+)g(1)p Fu(=)p Fx(2\))35792 11639 y Fq(d)36771
12121 y Fx(whic)-36 b(h)437 b(in)-36 b(tersects)438 b(it.)4317
13726 y(The)496 b(co{connectedness)g(of)h(a)f(set)g(of)h(b)36
b(onds)496 b(means)g(that)f(its)i(dual)e(is)i(a)f(connected)4317
15331 y(set)510 b(of)h Ft(R)8941 14849 y Fq(d)9991 15331
y Fx(\(with)f(the)f(usual)h(top)36 b(ology\).)810 b(Consider)510
b(the)g(co{b)36 b(oundary)510 b Fu(C)95 b Fx(\()p Fu(X)104
b Fx(\))510 b(of)h(a)4317 16936 y(set)434 b(of)g(b)36
b(onds)433 b Fu(X)538 b Fx(:)579 b Fu(C)95 b Fx(\()p
Fu(X)104 b Fx(\))369 b(=)g Fu(C)20089 17135 y Fs(1)20614
16936 y Fx(\()p Fu(X)104 b Fx(\))296 b Fr([)f Fu(C)25217
17135 y Fs(2)25742 16936 y Fx(\()p Fu(X)104 b Fx(\))434
b(where)11506 19842 y Fu(C)12437 20041 y Fs(1)12962 19842
y Fx(\()p Fu(X)104 b Fx(\))370 b(=)f Fr(f)p Fu(b)g Fr(2)f
Ft(L)20634 20041 y Fs(1)21455 19842 y Fr(n)295 b Fu(X)474
b Fx(:)369 b Fu(b)434 b Fx(has)f(1)h(endp)36 b(oin)-36
b(t)433 b(in)g(\244\()p Fu(X)104 b Fx(\))p Fr(g)11506
21779 y Fu(C)12437 21978 y Fs(2)12962 21779 y Fx(\()p
Fu(X)g Fx(\))370 b(=)f Fr(f)p Fu(b)g Fr(2)f Ft(L)20634
21978 y Fs(1)21455 21779 y Fr(n)295 b Fu(X)474 b Fx(:)369
b Fu(b)434 b Fx(has)f(2)h(endp)36 b(oin)-36 b(ts)433
b(in)g(\244\()p Fu(X)104 b Fx(\))p Fr(g)4317 24684 y
Fx(A)459 b(subset)f Fu(\260)485 b Fr(\275)412 b Ft(L)13256
24883 y Fs(1)14240 24684 y Fx(is)460 b(called)f(con)-36
b(tour)459 b(if)g(it)h(is)f(the)f(co{b)36 b(oundary)460
b(of)f(a)h(set)f(of)g(b)36 b(onds)4317 26289 y Fu(X)664
b Fx(and)559 b(if)i(it)e(is)h(co{connected.)956 b(When)559
b Fu(X)664 b Fx(is)560 b(\257nite,)591 b Fu(\260)631
b Fx(is)560 b(called)g(con)-36 b(tour)559 b(of)h(the)4317
27894 y(free)458 b(class)g(\(or)f(f{con)-36 b(tour\))457
b(and)f Fu(X)562 b Fx(will)459 b(b)36 b(e)456 b(denoted)h(b)-36
b(y)457 b(In)-36 b(t)221 b Fu(\260)72 b Fx(.)648 b(The)458
b(length)e(of)i Fu(\260)529 b Fx(is)4317 29499 y(de\257ned)432
b(as)11537 32404 y Fr(k)p Fu(\260)72 b Fr(k)369 b Fx(=)g
Fr(j)p Fu(C)16662 32603 y Fs(1)17187 32404 y Fx(\(In)-36
b(t)221 b Fu(\260)72 b Fx(\))p Fr(j)295 b Fx(+)f Fr(j)p
Fu(C)24099 32603 y Fs(2)24625 32404 y Fx(\(In)-36 b(t)220
b Fu(\260)72 b Fx(\))p Fr(j)1522 b Fx(if)435 b Fu(\260)505
b Fx(is)434 b(a)g(f{con)-36 b(tour)4317 35310 y(With)434
b(these)f(de\257nitions,)g(one)g(has)h(\([LMMRS)o(]\):)14827
38215 y Fu(Z)15812 37666 y Fs(f)16226 38215 y Fx(\()p
Fu(V)72 b(;)221 b(\257)18878 38414 y Fq(t)19274 38215
y Fu(;)g(q)48 b Fx(\))369 b(=)f Fu(q)23361 37666 y Fp(j)p
Fs(\244)24275 37789 y Fo(0)24736 37666 y Fs(\()p Fq(V)209
b Fs(\))p Fp(j)p Fs(+)p Fp(j)p Fq(\270)p Fs(\()p Fq(V)g
Fs(\))p Fp(j)29834 38215 y Fr(Z)106 b Fx(\()p Fu(V)288
b Fr(j)p Fu(')33676 38414 y Fq(f)34281 38215 y Fx(\))16034
41314 y Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p Fu(')19876
41513 y Fq(f)20481 41314 y Fx(\))369 b(=)26069 40052
y Fj(X)22736 42930 y Fp(f)q Fq(\260)23692 43053 y Fo(1)24153
42930 y Fq(;:::;\260)25943 43041 y Fn(n)26511 42930 y
Fp(g\275)p Fq(V)209 b Fp([)p Fq(C)63 b Fs(\()p Fq(V)209
b Fs(\))32104 39653 y Fq(n)31541 40052 y Fj(Y)31628 42851
y Fq(i)p Fs(=1)33460 41314 y Fu(')34312 41513 y Fq(f)34917
41314 y Fx(\()p Fu(\260)36098 41513 y Fq(i)36473 41314
y Fx(\))8197 b(\(12\))4317 45691 y(where)412 b(the)f(last)h(sum)f(runs)
f(o)-36 b(v)g(er)412 b(compatibles)g(families,)418 b(i.e.)412
b Fu(\260)36050 45890 y Fq(i)36676 45691 y Fr(\\)249
b Fu(\260)38486 45890 y Fq(j)39342 45691 y Fx(=)369 b
Fr(;)p Fx(,)416 b(and)411 b Fu(\270)p Fx(\()p Fu(V)289
b Fx(\))4317 47296 y(is)465 b(a)h(b)36 b(oundary)464
b(term)g(suc)-36 b(h)464 b(that)h Fr(j)p Fu(\270)p Fx(\()p
Fu(V)288 b Fx(\))p Fr(j)423 b(\267)887 b Fu(cte)464 b
Fr(j)p Fu(B)67 b Fx(\()p Fu(V)289 b Fx(\))p Fr(j)p Fx(.)672
b(The)465 b(activities)h Fu(')43612 47495 y Fq(f)44217
47296 y Fx(\()p Fu(\260)72 b Fx(\))465 b(of)4317 48901
y(con)-36 b(tours)433 b(are)h(giv)-36 b(en)434 b(b)-36
b(y)17875 51806 y Fu(')18727 52005 y Fq(f)19332 51806
y Fx(\()p Fu(\260)72 b Fx(\))368 b(=)h Fu(q)23465 51258
y Fp(\241)24542 50896 y Fo(1)p 24329 51057 833 40 v 24329
51605 a(2)p Fn(d)25295 51258 y Fp(k)p Fq(\260)52 b Fp(k)p
Fs(+)p Fq(\274)28076 50945 y Fo(0)28538 51258 y Fs(\(In)-26
b(t)156 b Fq(\260)52 b Fs(\))31220 51806 y Fu(e)31823
51258 y Fs(\242\()p Fq(\260)g Fs(\))45176 51806 y Fx(\(13\))4317
54712 y(where)434 b(\242\()p Fu(\260)72 b Fx(\))433 b(satis\257es)g
(the)g(b)36 b(ound:)19240 57945 y Fr(j)p Fx(\242\()p
Fu(\260)72 b Fx(\))p Fr(j)368 b(\267)h Fx(6)p Fu(q)25866
57289 y Fp(\241)27670 56916 y Fn(d)p Fm(\241)p Fo(1)p
26731 57088 3351 40 v 26731 57636 a(2)p Fn(d)p Fo(\(2)p
Fn(d)p Fm(\241)p Fo(1\))30491 57945 y Fr(k)p Fu(\260)72
b Fr(k)12610 b Fx(\(14\))4317 60851 y(This)453 b(implies)g(that)f(for)h
(large)g Fu(q)500 b Fx(the)452 b(free)h(energy)g Fu(f)142
b Fx(\()p Fu(')31944 61050 y Fq(f)32548 60851 y Fx(\))401
b(=)873 b(lim)34868 61682 y Fq(V)209 b Fp(!)p Fi(L)37156
61805 y Fo(1)39078 60328 y Fs(1)p 37751 60545 3126 54
v 37751 61309 a Fp(j)p Fs(\244)38665 61432 y Fo(0)39126
61309 y Fs(\()p Fq(V)g Fs(\))p Fp(j)41230 60851 y Fx(ln)221
b Fr(Z)106 b Fx(\()p Fu(V)289 b Fr(j)p Fu(')46378 61050
y Fq(f)46983 60851 y Fx(\))4317 63484 y(of)471 b(con)-36
b(tour)470 b(mo)36 b(del)470 b(b)36 b(eha)-36 b(v)g(es)471
b(lik)-36 b(e)471 b Fu(d)221 b(q)23336 62994 y Fp(\241)24201
62620 y Fn(d)p Fm(\241)p Fo(1)p 24200 62792 1473 40 v
24723 63341 a Fn(d)26180 63484 y Fx(+)320 b Fu(O)36 b
Fx(\()p Fu(q)29673 62994 y Fp(\241)30538 62547 y Fo(2\()p
Fn(d)p Fm(\241)p Fo(1\))p 30537 62792 2518 40 v 31583
63341 a Fn(d)33243 63484 y Fx(\).)688 b(W)-108 b(e)470
b(will)i(sho)-36 b(w)470 b(that)g(the)4317 65089 y(dominan)-36
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b(cal)564 b(Euler)e(c)-36 b(haracteristic)562 b Fu(\302)37635
64607 y Fs(f)38048 65089 y Fx(\()p Fu(\257)74 b(;)221
b(q)48 b Fx(\))562 b(shares)g(the)4317 66694 y(same)434
b(b)36 b(eha)-36 b(viour.)25253 70015 y(18)p eop
%%Page: 19 19
19 18 bop 6268 7306 a Fx(F)-108 b(or)383 b(that)g(purp)36
b(ose,)393 b(w)-36 b(e)383 b(will)i(follo)-36 b(w)385
b(the)e(same)g(strategy)h(as)g(in)f(as)h(in)f(the)g(pro)36
b(of)384 b(of)4317 8911 y(Theorem)f(4.)562 b(Namely)384
b(w)-36 b(e)383 b(consider)f(the)g(ev)-36 b(en)g(ts)383
b Fu(E)29974 9110 y Fq(f)30578 8911 y Fx(,)394 b Fu(E)460
b Fx(and)382 b Fu(E)36275 8429 y Fp(0)36968 8911 y Fx(de\257ned)f(in)i
(\(25{27\),)4317 10516 y(again)337 b(one)f(has)g Fu(\302)13012
10715 y Fs(0)13538 10516 y Fx(\()p Fu(n)p Fx(\))369 b(=)g(0)336
b(for)h Fu(n)369 b Fr(2)g Fu(E)23315 10715 y Fq(f)23919
10516 y Fx(,)356 b Fu(\302)25451 10715 y Fs(0)25977 10516
y Fx(\()p Fu(n)p Fx(\))369 b(=)g(1)p Fu(=)p Fx(2)337
b(for)f Fu(n)370 b Fr(2)e Fu(E)414 b Fx(and)336 b Fr(j)p
Fu(\302)41084 10715 y Fs(0)41609 10516 y Fx(\()p Fu(n)p
Fx(\))p Fr(j)369 b(\267)h Fx(1)p Fu(=)p Fx(2)4317 12121
y(for)486 b Fu(n)457 b Fr(2)f Fu(E)9972 11639 y Fp(0)10282
12121 y Fx(.)733 b(The)485 b(rest)g(of)g(the)g(pro)36
b(of)485 b(is)h(analogous)g(to)f(that)g(of)g(Theorem)h(4.)733
b(Only)4317 13726 y(some)434 b(estimates)g(ha)-36 b(v)g(e)434
b(to)f(b)36 b(e)434 b(c)-36 b(hanged,)433 b(namely)h(\(30\))g(no)-36
b(w)434 b(reads)12388 16226 y(Pr)o(\()p Fu(E)15325 15677
y Fp(0)15635 16226 y Fx(\))369 b Fr(\267)20189 14964
y Fj(X)17912 17842 y Fq(\260)52 b Fs(:)p Fq(\260)g Fp(3)p
Fs(0;)p Fp(j)159 b Fs(In)-26 b(t)156 b Fq(\260)52 b Fp(j\270)p
Fs(2)24605 16226 y Fx(Pr\()p Fu(\260)72 b Fx(\))368 b
Fr(\267)32096 14964 y Fj(X)29525 17842 y Fq(\260)52 b
Fs(:)p Fq(\260)g Fp(3)p Fs(0;)p Fp(k)r Fq(\260)g Fp(k\270)p
Fs(6)p Fq(d)p Fp(\241)p Fs(4)36808 16226 y Fu(')p Fx(\()p
Fu(\260)72 b Fx(\))16510 20597 y Fr(\267)18813 19335
y Fj(X)17912 22164 y Fq(m)p Fp(\270)p Fs(6)p Fq(d)p Fp(\241)p
Fs(4)21855 20597 y Fu(\272)22582 20049 y Fq(m)22498 20925
y(d)23469 19521 y Fj(\241)24078 20597 y Fu(q)24703 19941
y Fp(\241)26303 19567 y Fn(d)p Fm(\241)p Fo(1)p 25567
19739 2945 40 v 25567 20288 a(\(4)p Fn(d)p Fm(\241)p
Fo(2\))p Fn(d)28699 20597 y Fu(e)29302 20049 y Fs(6)p
Fq(q)30224 19407 y Fm(\241)31733 19100 y Fn(d)p Fm(\241)p
Fo(1)p 30997 19257 2945 33 v 30997 19787 a(\(4)p Fn(d)p
Fm(\241)p Fo(2\))p Fn(d)34185 19521 y Fj(\242)34793 19818
y Fq(m)16510 25679 y Fr(\267)369 b Fu(\272)18639 25130
y Fs(6)p Fq(d)p Fp(\241)p Fs(4)18555 26049 y Fq(d)20984
24781 y Fu(q)21609 24198 y Fp(\241)p Fs(\()22840 23825
y Fn(d)p Fm(\241)p Fo(1)p 22839 23997 1473 40 v 23361
24546 a Fn(d)24444 24198 y Fs(+)25511 23825 y Fn(d)p
Fm(\241)p Fo(1)p 25308 23997 1879 40 v 25308 24546 a(2)p
Fn(d)p Fm(\241)p Fo(1)27319 24198 y Fs(\))27741 24781
y Fu(e)28344 24299 y Fs(6\(6)p Fq(d)p Fp(\241)p Fs(4\))p
Fq(q)32154 23657 y Fm(\241)33663 23350 y Fn(d)p Fm(\241)p
Fo(1)p 32927 23507 2945 33 v 32927 24037 a(\(4)p Fn(d)p
Fm(\241)p Fo(2\))p Fn(d)p 20984 25374 15131 54 v 21768
27327 a Fx(1)295 b Fr(\241)h Fu(\272)24685 27526 y Fq(d)25224
27327 y Fu(q)25849 26670 y Fp(\241)27449 26297 y Fn(d)p
Fm(\241)p Fo(1)p 26713 26469 2945 40 v 26713 27018 a(\(4)p
Fn(d)p Fm(\241)p Fo(2\))p Fn(d)29845 27327 y Fu(e)30448
26943 y Fs(6)p Fq(q)31370 26301 y Fm(\241)32879 25994
y Fn(d)p Fm(\241)p Fo(1)p 32143 26151 2945 33 v 32143
26682 a(\(4)p Fn(d)p Fm(\241)p Fo(2\))p Fn(d)45176 25679
y Fx(\(15\))4317 29451 y(Here)574 b(w)-36 b(e)575 b(ha)-36
b(v)g(e)574 b(used)f Fu(\274)16619 28969 y Fs(0)17144
29451 y Fx(\(In)-36 b(t)221 b Fu(\260)72 b Fx(\))608
b Fr(\267)24011 28928 y Fs(1)p 23168 29146 2157 54 v
23168 29909 a(4)p Fq(d)p Fp(\241)p Fs(2)25679 29451 y
Fr(k)p Fu(\260)72 b Fr(k)574 b Fx(and)g(that)g Fu(\272)34684
28969 y Fq(m)34600 29797 y(d)36145 29451 y Fx(b)36 b(ounds)573
b(the)g(n)-36 b(um)g(b)36 b(er)4317 31056 y(of)647 b(con)-36
b(tours)646 b(of)h(length)g Fu(m)f Fx(that)g(con)-36
b(tain)646 b(a)h(giv)-36 b(en)647 b(p)36 b(oin)-36 b(t:)1004
b Fu(\272)36845 31255 y Fq(d)38030 31056 y Fx(can)647
b(b)36 b(e)646 b(b)36 b(ounded)4317 32661 y(b)-36 b(y)592
b Fu(\272)6925 32860 y Fq(d)8104 32661 y Fr(\267)639
b Fu(d)10452 32179 y Fs(2)10978 32661 y Fx(2)11628 32179
y Fs(4\()p Fq(d)p Fp(\241)p Fs(1\))14572 32661 y Fx(.)1054
b(T)-108 b(o)593 b(see)f(it,)633 b(w)-36 b(e)592 b(\257rst)g(observ)-36
b(e)592 b(that)g(the)g(n)-36 b(um)g(b)36 b(er)591 b(of)i
Fu(p)p Fx({cells)4317 34266 y(\()p Fu(x)p Fx(;)221 b
Fu(\276)6883 34465 y Fs(1)7410 34266 y Fu(e)8013 34465
y Fq(i)8333 34588 y Fo(1)8850 34266 y Fu(;)g(:::;)g(\276)11836
34465 y Fq(p)12367 34266 y Fu(e)12970 34465 y Fq(i)13290
34576 y Fn(p)13828 34266 y Fx(\))417 b(that)g(share)g(a)g(same)h(v)-36
b(ertex)418 b Fu(x)f Fx(equals)i(2)34908 33784 y Fq(p)35437
33191 y Fj(\241)36046 33677 y Fq(d)36051 34725 y(p)36530
33191 y Fj(\242)37139 34266 y Fx(:)570 b(2)38720 33784
y Fq(p)39667 34266 y Fx(stands)416 b(for)i(the)4317 36212
y(c)-36 b(hoice)598 b(for)g(the)f(signs)h(of)h(the)e
Fu(\276)48 b Fx('s)597 b(and)h(the)f(binomial)h(co)36
b(e\261cien)-36 b(t)39411 35136 y Fj(\241)40019 35622
y Fq(d)40025 36670 y(p)40504 35136 y Fj(\242)41710 36212
y Fx(stands)597 b(for)4317 37949 y(the)529 b(c)-36 b(hoice)530
b(of)g Fu(p)f Fx(v)-36 b(ectors)530 b(among)g(\()p Fu(e)23281
38148 y Fs(1)23806 37949 y Fu(;)221 b(:::;)g(e)26656
38148 y Fq(d)27198 37949 y Fx(\).)865 b(This)530 b(implies)g(\(b)-36
b(y)529 b(dualit)-36 b(y\))529 b(that)g(a)4317 39554
y(\()p Fu(d)205 b Fr(\241)g Fx(1\){cell)391 b(con)-36
b(tains)389 b(2)16724 39072 y Fq(d)p Fp(\241)p Fs(1)18856
39554 y Fx(v)-36 b(ertices)390 b(and)f(hence)f(that)h(the)g(n)-36
b(um)g(b)36 b(er)388 b(of)i(\()p Fu(d)205 b Fr(\241)g
Fx(1\){cells)4317 41159 y(connected)381 b(\(i.e.)h(sharing)f(at)g
(least)h(a)g(v)-36 b(ertex\))381 b(with)h(a)f(giv)-36
b(en)382 b(\()p Fu(d)188 b Fr(\241)g Fx(1\){cell)383
b(is)f(less)f(than)4317 42764 y(2)4967 42282 y Fs(\()p
Fq(d)p Fp(\241)p Fs(1\))7441 42764 y Fx(\()p Fu(d)p Fx(2)9273
42282 y Fs(\()p Fq(d)p Fp(\241)p Fs(1\))11960 42764 y
Fr(\241)213 b Fx(1\).)566 b(Finally)-108 b(,)402 b(one)394
b(uses)f(the)g(fact)h(that)f(for)h(an)-36 b(y)394 b(con)-36
b(tour)393 b(there)g(exist)4317 44369 y(a)370 b(path)f(going)h(through)
e(the)h(cen)-36 b(ter)369 b(of)h(ev)-36 b(ery)370 b(\()p
Fu(d)164 b Fr(\241)g Fx(1\){cell)370 b(of)g(its)g(dual)f(at)h(most)f(t)
-36 b(wice)4317 45975 y([Or].)6268 48082 y(The)434 b(cluster)f
(expansion)h(no)-36 b(w)434 b(giv)-36 b(es)14034 49809
y Fj(X)11780 52687 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69
b Fp(\\)p Fq(b)p Fp(6)p Fs(=)p Fp(;)18428 51071 y Fr(j)p
Fu(\301)19567 50523 y Fq(T)20301 51071 y Fx(\()p Fu(X)104
b Fx(\))p Fr(j)369 b(\267)24637 49995 y Fj(\241)25245
51071 y Fu(\272)25888 51270 y Fq(d)26428 51071 y Fu(g)48
b(q)27724 50415 y Fp(\241)29323 50041 y Fn(d)p Fm(\241)p
Fo(1)p 28587 50213 2945 40 v 28587 50762 a(\(4)p Fn(d)p
Fm(\241)p Fo(2\))p Fn(d)31720 51071 y Fu(e)32323 50523
y Fs(6)p Fq(q)33245 49881 y Fm(\241)34753 49574 y Fn(d)p
Fm(\241)p Fo(1)p 34017 49731 2945 33 v 34017 50261 a(\(4)p
Fn(d)p Fm(\241)p Fo(2\))p Fn(d)37205 49995 y Fj(\242)37814
50293 y Fs(4)p Fq(d)p Fp(\241)p Fs(2)45176 51071 y Fx(\(16\))4317
55657 y(for)434 b Fu(\272)6947 55856 y Fq(d)7486 55657
y Fu(g)48 b(q)8782 55000 y Fp(\241)10382 54627 y Fn(d)p
Fm(\241)p Fo(1)p 9646 54799 2945 40 v 9646 55348 a(\(4)p
Fn(d)p Fm(\241)p Fo(2\))p Fn(d)12778 55657 y Fu(e)13381
55175 y Fs(6)p Fq(q)14303 54533 y Fm(\241)15812 54226
y Fn(d)p Fm(\241)p Fo(1)p 15076 54383 2945 33 v 15076
54913 a(\(4)p Fn(d)p Fm(\241)p Fo(2\))p Fn(d)18633 55657
y Fu(<)368 b Fx(1,)435 b(leading)f(to)9077 59410 y(Pr)o(\()p
Fu(E)78 b Fx(\))369 b(=)f(2)p Fu(dq)16220 58862 y Fp(\241)17085
58415 y Fm(k)35 b Fo(\271)-441 b Fn(\260)43 b Fm(k)p
17085 58661 1325 40 v 17331 59209 a Fo(2)p Fn(d)18542
58862 y Fs(+)p Fq(\274)19846 58549 y Fo(0)20307 58862
y Fs(\(In)-26 b(t)190 b(\271)-504 b Fq(\260)52 b Fs(\))23211
59410 y Fx(exp)25419 56687 y Fj(8)25419 57883 y(<)25419
60274 y(:)26600 59410 y Fx(\242\()c(\271)-698 b Fu(\260)72
b Fx(\))295 b Fr(\241)33388 58149 y Fj(X)31066 61027
y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp(\\)33 b Fs(\271)-503
b Fq(\260)52 b Fp(6)p Fs(=)p Fp(;)37849 59410 y Fu(\301)38619
58862 y Fq(T)39353 59410 y Fx(\()p Fu(X)104 b Fx(\))41548
56687 y Fj(9)41548 57883 y(=)41548 60274 y(;)12889 64635
y Fx(=)368 b(2)p Fu(dq)16220 64087 y Fp(\241)17085 63713
y Fn(d)p Fm(\241)p Fo(1)p 17085 63885 1473 40 v 17607
64434 a Fn(d)18966 64635 y Fx(exp)21175 61912 y Fj(8)21175
63108 y(<)21175 65499 y(:)22356 64635 y Fx(\242\()48
b(\271)-698 b Fu(\260)71 b Fx(\))295 b Fr(\241)29143
63373 y Fj(X)26821 66252 y Fq(X)69 b Fs(:Supp)157 b Fq(X)69
b Fp(\\)33 b Fs(\271)-503 b Fq(\260)52 b Fp(6)p Fs(=)p
Fp(;)33605 64635 y Fu(\301)34375 64087 y Fq(T)35108 64635
y Fx(\()p Fu(X)104 b Fx(\))37303 61912 y Fj(9)37303 63108
y(=)37303 65499 y(;)45176 64635 y Fx(\(17\))25253 70015
y(19)p eop
%%Page: 20 20
20 19 bop 4317 7306 a Fx(and)7571 8683 y Fj(\257)7571
9480 y(\257)7571 10277 y(\257)7571 11074 y(\257)7571
11871 y(\257)7571 12668 y(\257)10336 10144 y(X)8014 13022
y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp(\\)33 b Fs(\271)-503
b Fq(\260)53 b Fp(6)p Fs(=)p Fp(;)14797 11406 y Fu(\301)15567
10857 y Fq(T)16301 11406 y Fx(\()p Fu(X)104 b Fx(\))18496
8683 y Fj(\257)18496 9480 y(\257)18496 10277 y(\257)18496
11074 y(\257)18496 11871 y(\257)18496 12668 y(\257)19308
11406 y Fr(\267)20710 10144 y Fj(X)20886 12973 y Fq(b)p
Fp(2)33 b Fs(\271)-503 b Fq(\260)25105 10144 y Fj(X)22850
13022 y Fq(X)69 b Fs(:Supp)157 b Fq(X)69 b Fp(\\)p Fq(b)p
Fp(6)p Fs(=)p Fp(;)29499 11406 y Fr(j)p Fu(\301)30638
10857 y Fq(T)31372 11406 y Fx(\()p Fu(X)104 b Fx(\))p
Fr(j)19308 15866 y(\267)369 b Fx(\(4)p Fu(d)295 b Fr(\241)h
Fx(2\)\()p Fu(\272)26471 16065 y Fq(d)27010 15866 y Fu(g)48
b Fx(\))28187 15317 y Fs(4)p Fq(d)p Fp(\241)p Fs(2)30398
15866 y Fu(q)31023 15317 y Fp(\241)31888 14944 y Fn(d)p
Fm(\241)p Fo(1)p 31887 15116 1473 40 v 32410 15665 a
Fn(d)33548 15866 y Fu(e)34151 15317 y Fs(6\(4)p Fq(d)p
Fp(\241)p Fs(2\))p Fq(q)37961 14675 y Fm(\241)39470 14369
y Fn(d)p Fm(\241)p Fo(1)p 38734 14526 2945 33 v 38734
15056 a(\(4)p Fn(d)p Fm(\241)p Fo(2\))p Fn(d)45176 15866
y Fx(\(18\))4317 18737 y(using)434 b Fr(k)48 b Fx(\271)-698
b Fu(\260)72 b Fr(k)369 b Fx(=)f(4)p Fu(d)296 b Fr(\241)f
Fx(2)434 b(and)f Fu(\274)18894 18255 y Fs(0)19419 18737
y Fx(\(In)-36 b(t)269 b(\271)-698 b Fu(\260)72 b Fx(\))369
b(=)f(1.)579 b(This)434 b(implies)15386 21863 y Fu(\302)16201
21314 y Fs(f)16614 21863 y Fx(\()p Fu(\257)17854 22062
y Fq(t)18249 21863 y Fu(;)221 b(q)48 b Fx(\))369 b(=)f
Fu(d)221 b(q)23233 21314 y Fp(\241)24098 20941 y Fn(d)p
Fm(\241)p Fo(1)p 24098 21113 1473 40 v 24620 21661 a
Fn(d)26053 21863 y Fx(+)295 b Fu(O)36 b Fx(\()p Fu(q)29521
21280 y Fp(\241)30386 20907 y Fn(d)p Fm(\241)p Fo(1)p
30385 21079 V 30908 21627 a Fn(d)31990 21280 y Fs([1+)34322
20918 y Fo(1)p 33586 21079 1879 40 v 33586 21627 a(4)p
Fn(d)p Fm(\241)p Fo(2)35597 21280 y Fs(])35914 21863
y Fx(\))8756 b(\(19\))4317 24734 y(giving)435 b(the)e(\257rst)g
(statemen)-36 b(t)433 b(of)h(the)f(theorem.)6268 26928
y(W)-108 b(e)507 b(no)-36 b(w)508 b(turn)d(to)j(the)e(pro)36
b(of)508 b(of)g(the)e(second)h(statemen)-36 b(t)507 b(of)g(the)g
(theorem.)799 b(W)-108 b(e)4317 28533 y(\257rst)382 b(de\257ne)g(the)h
(con)-36 b(tours)382 b(of)i(the)f(wired)g(class.)562
b(A)383 b(subset)g Fu(\260)440 b Fr(\275)370 b Ft(L)37389
28732 y Fs(1)38297 28533 y Fx(is)383 b(called)h(con)-36
b(tour)4317 30138 y(if)321 b(it)f(is)g(the)f(co{b)36
b(oundary)320 b(of)h(a)f(set)g(of)g(b)36 b(onds)319 b
Fu(X)425 b Fx(and)319 b(if)i(it)f(is)g(co{connected.)540
b(When)320 b Fu(X)4317 31743 y Fx(is)432 b(in\257nite,)g
Fu(\260)504 b Fx(is)432 b(called)h(con)-36 b(tour)431
b(of)i(the)e(wired)h(class)h(\(or)e(w{con)-36 b(tour\).)578
b(The)432 b(unique)4317 33348 y(in\257nite)440 b(comp)36
b(onen)-36 b(t)439 b(of)i Ft(L)17760 33547 y Fs(1)18586
33348 y Fr(n)300 b Fu(\260)512 b Fx(is)441 b(denoted)e(b)-36
b(y)440 b(Ext)222 b Fu(\260)72 b Fx(.)599 b(The)440 b(length)g(of)h
Fu(\260)512 b Fx(is)441 b(de\257ned)4317 34953 y(b)-36
b(y)10850 36558 y Fr(k)p Fu(\260)72 b Fr(k)369 b Fx(=)g
Fr(j)p Fu(C)15975 36757 y Fs(1)16500 36558 y Fx(\(Ext)222
b Fu(\260)72 b Fx(\))p Fr(j)295 b Fx(+)f Fr(j)p Fu(C)23828
36757 y Fs(2)24354 36558 y Fx(\(Ext)221 b Fu(\260)72
b Fx(\))p Fr(j)1522 b Fx(if)434 b Fu(\260)506 b Fx(is)434
b(a)g(w{con)-36 b(tour)4317 38856 y(With)434 b(these)f(de\257nitions,)g
(one)g(has)h(\([LMMRS)o(]\):)16010 41727 y Fu(Z)16995
41179 y Fs(w)17743 41727 y Fx(\()p Fu(V)72 b(;)221 b(\257)20395
41926 y Fq(t)20792 41727 y Fu(;)g(q)48 b Fx(\))368 b(=)h
Fu(q)48 b Fx(\()p Fu(e)25988 41179 y Fq(\257)e Fp(\241)p
Fs(1)27818 41727 y Fx(\))28324 41179 y Fp(j)p Fq(V)209
b Fp(j)29659 41727 y Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p
Fu(')33501 41926 y Fq(w)34256 41727 y Fx(\))17402 44826
y Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p Fu(')21244 45025
y Fq(w)21999 44826 y Fx(\))368 b(=)26161 43564 y Fj(X)24254
46442 y Fp(f)p Fq(\260)25209 46565 y Fo(1)25670 46442
y Fq(;:::;\260)27460 46553 y Fn(n)28028 46442 y Fp(g)q(\275)p
Fq(V)30772 43165 y(n)30209 43564 y Fj(Y)30296 46363 y
Fq(i)p Fs(=1)32128 44826 y Fu(')32980 45025 y Fq(w)33734
44826 y Fx(\()p Fu(\260)34915 45025 y Fq(i)35290 44826
y Fx(\))9380 b(\(20\))4317 49169 y(where)499 b(the)g(last)g(sum)g(runs)
f(o)-36 b(v)g(er)499 b(compatibles)h(families,)517 b(i.e.)500
b Fu(\260)36850 49368 y Fq(i)37565 49169 y Fr(\\)339
b Fu(\260)39465 49368 y Fq(j)40432 49169 y Fx(=)480 b
Fr(;)500 b Fx(and)e(the)4317 50774 y(activities)435 b
Fu(')10704 50973 y Fq(w)11459 50774 y Fx(\()p Fu(\260)72
b Fx(\))433 b(of)h(con)-36 b(tours)433 b(are)h(giv)-36
b(en)434 b(b)-36 b(y)19996 53822 y Fu(')20848 54021 y
Fq(w)21603 53822 y Fx(\()p Fu(\260)72 b Fx(\))368 b(=)h
Fu(q)25736 53273 y Fp(\241)26813 52911 y Fo(1)p 26600
53072 833 40 v 26600 53620 a(2)p Fn(d)27565 53273 y Fp(k)q
Fq(\260)52 b Fp(k)29098 53822 y Fu(e)29701 53273 y Fs(\242\()p
Fq(\260)g Fs(\))45176 53822 y Fx(\(21\))4317 56693 y(where)434
b(\242\()p Fu(\260)72 b Fx(\))433 b(satis\257es)g(the)g(b)36
b(ound:)20712 59740 y Fr(j)p Fx(\242\()p Fu(\260)72 b
Fx(\))p Fr(j)368 b(\267)i Fx(9)p Fu(q)27339 59191 y Fp(\241)28204
58829 y Fo(1)p 28203 58990 406 40 v 28203 59539 a(2)29018
59740 y Fr(k)q Fu(\260)72 b Fr(k)14082 b Fx(\(22\))4317
62611 y(This)427 b(implies)g(that)f(for)h(large)g Fu(q)474
b Fx(the)426 b(free)g(energy)h Fu(f)142 b Fx(\()p Fu(')31709
62810 y Fq(w)32463 62611 y Fx(\))369 b(=)840 b(lim)34719
63442 y Fq(V)209 b Fp(!)p Fi(L)37007 63565 y Fo(1)38929
62088 y Fs(1)p 37601 62305 3126 54 v 37601 63069 a Fp(j)p
Fs(\244)38515 63192 y Fo(0)38976 63069 y Fs(\()p Fq(V)g
Fs(\))p Fp(j)41081 62611 y Fx(ln)221 b Fr(Z)106 b Fx(\()p
Fu(V)288 b Fr(j)p Fu(')46228 62810 y Fq(w)46983 62611
y Fx(\))4317 65089 y(of)412 b(the)e(con)-36 b(tour)411
b(mo)36 b(del)411 b(b)36 b(eha)-36 b(v)g(es)411 b(lik)-36
b(e)412 b Fu(d)221 b(q)25257 64599 y Fp(\241)26132 64237
y Fo(1)p 26121 64398 427 40 v 26121 64946 a Fn(d)26985
65089 y Fx(+)249 b Fu(O)36 b Fx(\()p Fu(q)30407 64599
y Fp(\241)31282 64237 y Fo(2)p 31271 64398 V 31271 64946
a Fn(d)31886 65089 y Fx(\).)571 b(W)-108 b(e)411 b(will)h(sho)-36
b(w)411 b(that)f(\(up)g(to)4317 66694 y(the)489 b(sign\))g(the)g(lo)36
b(cal)490 b(Euler)f(c)-36 b(haracteristic)490 b Fu(\302)27682
66212 y Fs(w)28429 66694 y Fx(\()p Fu(\257)74 b(;)221
b(q)48 b Fx(\))489 b(shares)g(the)g(same)g(b)36 b(eha)-36
b(viour.)25253 70015 y(20)p eop
%%Page: 21 21
21 20 bop 4317 7306 a Fx(This)604 b(fact)f(migh)-36 b(t)603
b(b)36 b(e)603 b(seen)g(as)h(follo)-36 b(ws.)1089 b(The)603
b(\257rst)f(excitations)i(of)g(the)f(o)36 b(ccupied)4317
8911 y(ground)479 b(state)g(con\257guration)g(consist)g(of)h(empt)-36
b(y)479 b(b)36 b(onds)479 b(in)g(the)g(\\sea")h(of)g(o)36
b(ccupied)4317 10516 y(ones.)564 b(Eac)-36 b(h)389 b(excitation)h(giv)
-36 b(es)390 b(a)g(con)-36 b(tribution)388 b(to)h Fu(\274)30759
10034 y Fq(d)p Fp(\241)p Fs(1)32889 10516 y Fx(and)g(the)g(n)-36
b(um)g(b)36 b(er)387 b(of)j(excita-)4317 12121 y(tions)405
b(scales)h(lik)-36 b(e)406 b(the)e(v)-36 b(olume,)411
b(giving)406 b(that)f(the)f(Euler)h(c)-36 b(haracteristic)405
b(b)36 b(eha)-36 b(v)g(es)405 b(lik)-36 b(e)4317 13726
y(\()p Fr(\241)p Fx(1\))7012 13244 y Fq(d)p Fp(\241)p
Fs(1)8754 13726 y Fu(O)36 b Fx(\()p Fu(q)10915 13236
y Fp(\241)11790 12874 y Fo(1)p 11779 13035 427 40 v 11779
13583 a Fn(d)12394 13726 y Fx(\).)753 b(T)-108 b(o)492
b(compute)f(the)h(co)36 b(e\261cien)-36 b(t)492 b(w)-36
b(e)492 b(will)h(consider)f(the)f(expression)4317 15331
y(\(6\))434 b(of)g(the)f(lo)36 b(cal)435 b(Euler)e(c)-36
b(haracteristic)434 b Fu(\302)25498 15530 y Fq(x)26083
15331 y Fx(\()p Fu(n)p Fx(\).)6268 17466 y(Let)641 b(us)h(in)-36
b(tro)36 b(duce)641 b(the)g Fu(p)p Fx({neigh)-36 b(b)36
b(orho)g(o)g(d)642 b(of)g(a)g(site)g Fu(x)724 b Fx(=)f(\()p
Fu(x)38822 17665 y Fs(1)39348 17466 y Fu(;)221 b(:)g(:)g(:)i(;)e(x)
42999 17665 y Fq(d)43540 17466 y Fx(\),)694 b Fu(p)723
b Fx(=)4317 19071 y(1)p Fu(;)221 b(:)g(:)g(:)j(;)d(d)p
Fx(,)521 b(as)503 b Fr(N)12194 19270 y Fq(p)12723 19071
y Fx(\()p Fu(x)p Fx(\))486 b(=)g Fr(f)p Fu(y)535 b Fx(=)486
b(\()p Fu(y)20929 19270 y Fs(1)21455 19071 y Fu(;)221
b(:)g(:)g(:)j(;)d(y)25002 19270 y Fq(d)25542 19071 y
Fx(\))486 b(:)27382 18075 y Fj(P)28784 18426 y Fq(d)28784
19459 y(i)p Fs(=1)30584 19071 y Fr(j)p Fu(x)31692 19270
y Fq(i)32410 19071 y Fr(\241)342 b Fu(y)34419 19270 y
Fq(i)34795 19071 y Fr(j)487 b Fx(=)f Fu(p)p Fr(g)502
b Fx(and)h(recall)g(that)4317 20676 y Fu(S)5194 20194
y Fq(d)5734 20676 y Fx(\()p Fu(x)p Fx(\))433 b(is)h(the)f(set)h(of)g
(the)f(2)17868 20194 y Fq(d)18408 20676 y Fx({cells)h(that)g(con)-36
b(tain)433 b(the)g(site)h Fu(x)p Fx(.)6268 22811 y(T)-108
b(o)434 b(compute)f Fr(h)p Fu(\302)14790 23010 y Fs(0)15315
22811 y Fr(i)g Fx(w)-36 b(e)434 b(will)h(consider)e(the)g(follo)-36
b(wing)436 b(ev)-36 b(en)g(ts)6714 25269 y Fu(E)7677
25468 y Fq(w)8801 25269 y Fx(=)10181 24193 y Fj(\251)10956
25269 y Fu(n)369 b Fr(2)g(f)p Fx(0)p Fu(;)221 b Fx(1)p
Fr(g)16566 24720 y Fq(V)17749 25269 y Fx(:)591 b(all)434
b(the)f(b)36 b(onds)433 b(of)h(the)369 b Fu(d)p Fx({cells)434
b(b)36 b(elonging)434 b(to)222 b Fu(S)42500 24720 y Fq(d)43040
25269 y Fx(\(0\))10956 27322 y(are)434 b(o)36 b(ccupied)18074
26246 y Fj(\252)45176 27322 y Fx(\(23\))6714 29400 y
Fu(E)7755 28852 y Fp(0)7677 29729 y Fq(w)8801 29400 y
Fx(=)10181 28324 y Fj(\251)10956 29400 y Fu(n)369 b Fr(2)g(f)p
Fx(0)p Fu(;)221 b Fx(1)p Fr(g)16566 28852 y Fq(V)17749
29400 y Fx(:)591 b(there)433 b(is)g(exactly)j(one)d(empt)-36
b(y)433 b(b)36 b(ond)433 b(in)h(the)368 b Fu(d)p Fx({cells)10956
31488 y(b)36 b(elonging)434 b(to)222 b Fu(S)19100 30939
y Fq(d)19639 31488 y Fx(\(0\))f(and)434 b(this)f(b)36
b(ond)433 b(has)g(no)h(endp)36 b(oin)-36 b(t)220 b(in)h
Fr(N)41604 31687 y Fq(d)42144 31488 y Fx(\(0\);)10956
33425 y(in)433 b(addition,)h(all)h(other)e(b)36 b(onds)433
b(of)h(the)368 b Fu(d)p Fx({cells)223 b(that)433 b(con)-36
b(tain)433 b(this)10956 35479 y(b)36 b(ond)433 b(are)h(o)36
b(ccupied)21361 34403 y Fj(\252)45176 35479 y Fx(\(24\))7391
37556 y Fu(E)447 b Fx(=)10181 36480 y Fj(\251)10956 37556
y Fu(n)369 b Fr(2)g(f)p Fx(0)p Fu(;)221 b Fx(1)p Fr(g)16566
37008 y Fq(V)17749 37556 y Fx(:)591 b(there)433 b(is)g(exactly)j(one)d
(empt)-36 b(y)433 b(b)36 b(ond)433 b(in)h(the)368 b Fu(d)p
Fx({cells)10956 39644 y(b)36 b(elonging)434 b(to)222
b Fu(S)19100 39096 y Fq(d)19639 39644 y Fx(\(0\))f(and)434
b(this)f(b)36 b(ond)433 b(has)g(one)h(endp)36 b(oin)-36
b(t)220 b(in)i Fr(N)42183 39843 y Fq(d)42722 39644 y
Fx(\(0\);)10956 41581 y(in)433 b(addition,)h(all)h(other)e(b)36
b(onds)433 b(of)h(the)368 b Fu(d)p Fx({cells)223 b(that)433
b(con)-36 b(tain)433 b(this)10956 43635 y(b)36 b(ond)433
b(are)h(o)36 b(ccupied)21361 42559 y Fj(\252)45176 43635
y Fx(\(25\))4317 46092 y(and)433 b(the)g(complemen)-36
b(tary)434 b(ev)-36 b(en)g(t)15519 48550 y Fu(E)16560
48001 y Fp(0)17239 48550 y Fx(=)18620 47474 y Fj(\251)19395
48550 y Fu(n)369 b Fr(2)g(f)p Fx(0)p Fu(;)221 b Fx(1)p
Fr(g)25005 48001 y Fq(V)26114 48550 y Fr(n)295 b Fx(\()p
Fu(E)373 b Fr([)295 b Fu(E)31059 48749 y Fq(w)32108 48550
y Fr([)g Fu(E)34330 48001 y Fp(0)34252 48878 y Fq(w)35006
48550 y Fx(\))35512 47474 y Fj(\252)45176 48550 y Fx(\(26\))6268
51537 y(W)-108 b(e)434 b(ha)-36 b(v)g(e)14510 53995 y
Fu(\302)15325 54194 y Fs(0)15851 53995 y Fx(\()p Fu(n)p
Fx(\))369 b(=)f(0)5354 b(if)434 b Fu(n)369 b Fr(2)g Fu(E)29947
54194 y Fq(w)31135 53995 y Fx(or)433 b(if)i Fu(n)369
b Fr(2)f Fu(E)37357 53446 y Fp(0)37279 54323 y Fq(w)45176
53995 y Fx(\(27\))14510 56915 y Fu(\302)15325 57114 y
Fs(0)15851 56915 y Fx(\()p Fu(n)p Fx(\))h(=)19521 56016
y(\()p Fr(\241)p Fx(1\))22216 55534 y Fq(d)p Fp(\241)p
Fs(1)p 19521 56609 4437 54 v 21145 57826 a Fx(2)21795
57442 y Fq(d)25392 56915 y Fx(if)434 b Fu(n)369 b Fr(2)g
Fu(E)15229 b Fx(\(28\))13772 59392 y Fr(j)p Fu(\302)14956
59591 y Fs(0)15482 59392 y Fx(\()p Fu(n)p Fx(\))p Fr(j)369
b(\267)g Fx(1)5332 b(if)434 b Fu(n)369 b Fr(2)g Fu(E)30025
58844 y Fp(0)45176 59392 y Fx(\(29\))6268 62380 y(Then,)10992
65597 y Fr(h)p Fu(\302)12324 65796 y Fs(0)12850 65597
y Fr(i)13366 64951 y Fs(w)14336 65597 y Fx(\()p Fu(V)72
b(;)221 b(\257)74 b(;)221 b(q)48 b Fx(\))369 b(=)20658
64698 y(\()p Fr(\241)p Fx(1\))23353 64216 y Fq(d)p Fp(\241)p
Fs(1)p 20658 65291 V 22281 66508 a Fx(2)22931 66124 y
Fq(d)25449 65597 y Fx(Pr\()p Fu(E)78 b Fx(\))294 b(+)31069
64335 y Fj(X)30494 67170 y Fq(n)p Fs(:)p Fq(n)p Fp(2)p
Fq(E)33264 66918 y Fm(0)33562 65597 y Fx([)p Fu(\302)34738
65796 y Fs(0)35264 65597 y Fx(\()p Fu(n)p Fx(\)])221
b(Pr\()p Fu(n)p Fx(\))4363 b(\(30\))25253 70015 y(21)p
eop
%%Page: 22 22
22 21 bop 4317 7306 a Fx(with)17538 7417 y Fj(\257)17538
8214 y(\257)17538 9011 y(\257)17538 9808 y(\257)17538
10605 y(\257)18555 8479 y(X)17981 11314 y Fq(n)p Fs(:)p
Fq(n)p Fp(2)p Fq(E)20751 11062 y Fm(0)21049 9741 y Fx([)p
Fu(\302)22225 9940 y Fs(0)22751 9741 y Fx(\()p Fu(n)p
Fx(\)])221 b(Pr\()p Fu(n)p Fx(\))28300 7417 y Fj(\257)28300
8214 y(\257)28300 9011 y(\257)28300 9808 y(\257)28300
10605 y(\257)29112 9741 y Fr(\267)369 b Fx(Pr\()p Fu(E)33452
9193 y Fp(0)33762 9741 y Fx(\))10908 b(\(31\))4317 13307
y(T)-108 b(aking)575 b(in)-36 b(to)573 b(accoun)-36 b(t)573
b(that)g(for)h(an)-36 b(y)574 b(con\257guration)g Fu(n)607
b Fr(2)g Fu(E)36131 12825 y Fp(0)37015 13307 y Fx(there)573
b(is)g(at)h(least)g(a)4317 14912 y(con)-36 b(tour)450
b Fu(\260)522 b Fx(with)450 b(length)f Fr(k)p Fu(\260)72
b Fr(k)398 b(\270)f Fx(4,)455 b(w)-36 b(e)450 b(estimate)g(this)g
(probabilit)-36 b(y)450 b(b)-36 b(y)450 b(P)-36 b(eierls)451
b(t)-36 b(yp)36 b(e)4317 16518 y(argumen)-36 b(ts)433
b(as)h(follo)-36 b(ws)10868 19610 y(Pr\()p Fu(E)13806
19061 y Fp(0)14116 19610 y Fx(\))368 b Fr(\267)18120
18348 y Fj(X)16393 21226 y Fq(\260)52 b Fs(:)p Fq(\260)g
Fp(3)p Fs(0;)p Fp(k)q Fq(\260)g Fp(k)q(\270)p Fs(4)21988
19610 y Fx(Pr\()p Fu(\260)72 b Fx(\))369 b Fr(\267)28637
18348 y Fj(X)26909 21226 y Fq(\260)52 b Fs(:)p Fq(\260)g
Fp(3)p Fs(0;)p Fp(k)r Fq(\260)g Fp(k\270)p Fs(4)32505
19610 y Fu(')33357 19809 y Fq(w)34111 19610 y Fx(\()p
Fu(\260)72 b Fx(\))14990 24498 y Fr(\267)16451 23236
y Fj(X)16393 26042 y Fq(m)p Fp(\270)p Fs(4)18649 24498
y Fu(\272)19292 24697 y Fq(d)19831 23949 y(m)20718 23422
y Fj(\241)21327 24498 y Fu(q)21952 23949 y Fp(\241)23030
23587 y Fo(1)p 22816 23748 833 40 v 22816 24297 a(2)p
Fn(d)23837 24498 y Fu(e)24440 23949 y Fs(9)p Fq(q)25362
23544 y Fm(\241)26135 23283 y Fo(1)p 26135 23394 406
33 v 26135 23854 a(2)26784 23422 y Fj(\242)27393 23719
y Fq(m)28649 24498 y Fr(\267)370 b Fu(\272)30695 24697
y Fq(d)31234 23949 y Fs(4)33385 23599 y Fu(q)34010 23109
y Fp(\241)34885 22747 y Fo(2)p 34874 22908 427 40 v 34874
23456 a Fn(d)35489 23599 y Fu(e)36092 23117 y Fs(36)p
Fq(q)37484 22711 y Fm(\241)38460 22451 y Fo(1)p 38257
22562 812 33 v 38257 23022 a(12)p 31892 24192 8913 54
v 31892 25830 a Fx(1)296 b Fr(\241)f Fu(\272)34809 26029
y Fq(d)35348 25830 y Fu(q)35973 25339 y Fp(\241)37051
24977 y Fo(1)p 36837 25138 833 40 v 36837 25687 a(2)p
Fn(d)37858 25830 y Fu(e)38461 25446 y Fs(9)p Fq(q)39383
25040 y Fm(\241)40156 24780 y Fo(1)p 40156 24891 406
33 v 40156 25351 a(2)45176 24498 y Fx(\(32\))4317 29339
y(pro)-36 b(vided)433 b Fu(\272)10307 29538 y Fq(d)10846
29339 y Fu(q)11471 28849 y Fp(\241)12549 28487 y Fo(1)p
12335 28648 833 40 v 12335 29196 a(2)p Fn(d)13356 29339
y Fu(e)13959 28857 y Fs(9)p Fq(q)14881 28452 y Fm(\241)15654
28191 y Fo(1)p 15654 28302 406 33 v 15654 28762 a(2)16672
29339 y Fu(<)369 b Fx(1.)6268 31542 y(On)492 b(the)g(other)h(hand,)507
b(in)493 b(order)f(to)h(estimate)g(the)g(probabilit)-36
b(y)493 b(Pr)o(\()p Fu(E)78 b Fx(\))493 b(w)-36 b(e)493
b(let)541 b(~)-698 b Fu(\260)4317 33147 y Fx(to)434 b(b)36
b(e)433 b(the)g(dual)h(of)g(the)f(o)36 b(ccupied)433
b(b)36 b(ond.)578 b(Then)11697 39508 y(Pr)o(\()p Fu(E)78
b Fx(\))369 b(=)16520 38432 y Fj(\243)17207 38609 y Fx(\()p
Fr(\241)p Fx(1\))19902 38127 y Fq(d)p Fp(\241)p Fs(1)p
17207 39202 4437 54 v 18830 40419 a Fx(2)19480 40035
y Fq(d)21776 39508 y Fx(\(2)22932 38959 y Fq(d)23472
39508 y Fu(d)p Fx(\))24654 38432 y Fj(\244)27137 35757
y(X)25340 38635 y Fp(f)p Fq(\260)26295 38758 y Fo(1)26756
38635 y Fq(;:::;\260)28546 38746 y Fn(n)29114 38635 y
Fp(g)q(\276)33 b Fs(~)-503 b Fq(\260)31638 35359 y(n)31075
35757 y Fj(Y)31162 38557 y Fq(i)p Fs(=1)32994 37019 y
Fu(')33846 37218 y Fq(w)34600 37019 y Fx(\()p Fu(\260)35781
37218 y Fq(i)36156 37019 y Fx(\))p 25340 39202 11323
54 v 28450 40419 a Fr(Z)106 b Fx(\()p Fu(V)288 b Fr(j)p
Fu(')32292 40618 y Fq(w)33046 40419 y Fx(\))15509 45857
y(=)16520 44781 y Fj(\243)17074 45857 y Fx(\()p Fr(\241)p
Fx(1\))19769 45308 y Fq(d)p Fp(\241)p Fs(1)21511 45857
y Fu(d)22187 44781 y Fj(\244)22961 45857 y Fu(')23813
46056 y Fq(w)24568 45857 y Fx(\()48 b(~)-698 b Fu(\260)72
b Fx(\))29354 42106 y Fj(X)26460 44985 y Fp(f)p Fq(\260)27415
45108 y Fo(1)27876 44985 y Fq(;:::;\260)29666 45096 y
Fn(n)30234 44985 y Fp(g)p Fq(;\260)31450 45120 y Fn(i)31801
44985 y Fp(\\)33 b Fs(~)-503 b Fq(\260)52 b Fs(=)p Fp(;)34952
41708 y Fq(n)34389 42106 y Fj(Y)34477 44906 y Fq(i)p
Fs(=1)36308 43368 y Fu(')37160 43567 y Fq(w)37914 43368
y Fx(\()p Fu(\260)39095 43567 y Fq(i)39470 43368 y Fx(\))p
26460 45551 13518 54 v 30666 46768 a Fr(Z)106 b Fx(\()p
Fu(V)289 b Fr(j)p Fu(')34509 46967 y Fq(w)35263 46768
y Fx(\))45176 45857 y(\(33\))4317 49636 y(The)408 b(factor)g(2)11310
49154 y Fq(d)11850 49636 y Fu(d)f Fx(stems)g(from)h(the)f(fact)h(that)e
(there)h(are)h(2)33213 49154 y Fq(d)33753 49636 y Fu(d)f
Fx(b)36 b(onds)406 b(in)i(the)f Fu(d)p Fx({cells)h(of)4317
51241 y Fu(S)5194 50759 y Fq(d)5734 51241 y Fx(\(0\))349
b(that)f(con)-36 b(tain)349 b(one)g(endp)36 b(oin)-36
b(t)348 b(in)h(the)f Fu(d)h Fx({neigh)-36 b(b)36 b(ourho)g(o)g(d)348
b Fr(N)37773 51440 y Fq(d)38313 51241 y Fx(\(0\))h(of)g(the)g(origin.)
6268 53444 y(W)-108 b(e)597 b(will)h(compute)d(this)i(last)g(ratio)g
(with)g(cluster)f(expansion)h(b)-36 b(y)596 b(in)-36
b(tro)36 b(ducing)4317 55049 y(clusters)562 b Fu(X)667
b Fx(as)563 b(m)-36 b(ulti-indexes)562 b(de\257ned)e(on)i(the)g(sets)g
(of)h(wired)g(con)-36 b(tours)561 b(and)h(the)4317 56654
y(corresp)36 b(onding)433 b(truncated)g(functionals:)16370
60247 y Fu(\301)17140 59698 y Fq(T)17140 60575 y(w)17894
60247 y Fx(\()p Fu(X)104 b Fx(\))369 b(=)23144 59348
y Fu(a)p Fx(\()p Fu(X)104 b Fx(\))p 21972 59941 5223
54 v 21972 60233 a Fj(Y)22552 63023 y Fq(\260)23890 61495
y Fu(X)g Fx(\()p Fu(\260)72 b Fx(\)!)27548 58985 y Fj(Y)28129
61774 y Fq(\260)29467 60247 y Fu(')30319 60446 y Fq(w)31074
60247 y Fx(\()p Fu(X)104 b Fx(\))33269 59698 y Fq(X)69
b Fs(\()p Fq(\260)52 b Fs(\))45176 60247 y Fx(\(34\))25253
70015 y(22)p eop
%%Page: 23 23
23 22 bop 6268 7306 a Fx(By)473 b(taking)h(in)-36 b(to)472
b(accoun)-36 b(t)473 b(the)f(expression)h(\(21\))g(and)f(that)g
Fr(k)49 b Fx(\271)-699 b Fu(\260)72 b Fr(k)436 b Fx(=)f(2,)483
b(w)-36 b(e)473 b(get)g(as)4317 8911 y(a)434 b(result)f(of)i(cluster)e
(expansion)8816 13294 y(Pr)o(\()p Fu(E)78 b Fx(\))369
b(=)14008 12218 y Fj(\243)14562 13294 y Fx(\()p Fr(\241)p
Fx(1\))17257 12745 y Fq(d)p Fp(\241)p Fs(1)18999 13294
y Fu(d)19675 12218 y Fj(\244)20228 13294 y Fu(q)20853
12745 y Fp(\241)21718 12298 y Fm(k)34 b Fo(\271)-441
b Fn(\260)43 b Fm(k)p 21717 12544 1325 40 v 21963 13093
a Fo(2)p Fn(d)23451 13294 y Fx(exp)25660 10571 y Fj(8)25660
11766 y(<)25660 14157 y(:)26841 13294 y Fx(\242\()48
b(\271)-698 b Fu(\260)71 b Fx(\))295 b Fr(\241)33628
12032 y Fj(X)31307 14910 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69
b Fp(\\)33 b Fs(\271)-503 b Fq(\260)52 b Fp(6)p Fs(=)p
Fp(;)38090 13294 y Fu(\301)38860 12745 y Fq(T)38860 13622
y(w)39614 13294 y Fx(\()p Fu(X)104 b Fx(\))41809 10571
y Fj(9)41809 11766 y(=)41809 14157 y(;)12628 18519 y
Fx(=)14008 17443 y Fj(\243)14562 18519 y Fx(\()p Fr(\241)p
Fx(1\))17257 17970 y Fq(d)p Fp(\241)p Fs(1)18999 18519
y Fu(d)19675 17443 y Fj(\244)20228 18519 y Fu(q)20853
17970 y Fp(\241)21728 17608 y Fo(1)p 21717 17769 427
40 v 21717 18317 a Fn(d)22553 18519 y Fx(exp)24762 15795
y Fj(8)24762 16991 y(<)24762 19382 y(:)25943 18519 y
Fx(\242\()48 b(\271)-698 b Fu(\260)71 b Fx(\))295 b Fr(\241)32730
17257 y Fj(X)30409 20135 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69
b Fp(\\)33 b Fs(\271)-503 b Fq(\260)52 b Fp(6)p Fs(=)p
Fp(;)37192 18519 y Fu(\301)37962 17970 y Fq(T)37962 18847
y(w)38716 18519 y Fx(\()p Fu(X)104 b Fx(\))40911 15795
y Fj(9)40911 16991 y(=)40911 19382 y(;)45176 18519 y
Fx(\(35\))4317 22901 y(and)12700 24303 y Fj(\257)12700
25100 y(\257)12700 25897 y(\257)12700 26694 y(\257)12700
27491 y(\257)12700 28288 y(\257)15464 25764 y(X)13143
28642 y Fq(X)69 b Fs(:Supp)156 b Fq(X)69 b Fp([)33 b
Fs(\271)-503 b Fq(\260)52 b Fp(6)p Fs(=)p Fp(;)19926
27026 y Fu(\301)20696 26477 y Fq(T)20696 27354 y(w)21450
27026 y Fx(\()p Fu(X)104 b Fx(\))23645 24303 y Fj(\257)23645
25100 y(\257)23645 25897 y(\257)23645 26694 y(\257)23645
27491 y(\257)23645 28288 y(\257)24457 27026 y Fr(\267)25859
25764 y Fj(X)26035 28593 y Fq(b)p Fp(2)33 b Fs(\271)-503
b Fq(\260)30254 25764 y Fj(X)27999 28642 y Fq(X)69 b
Fs(:Supp)157 b Fq(X)69 b Fp(\\)p Fq(b)p Fp(6)p Fs(=)p
Fp(;)34648 27026 y Fr(j)p Fu(\301)35787 26477 y Fq(T)35787
27354 y(w)36541 27026 y Fx(\()p Fu(X)104 b Fx(\))p Fr(j)24457
31170 y(\267)369 b Fx(2\()p Fu(\271)27798 31369 y Fq(d)28338
31170 y Fu(g)48 b(q)29634 30622 y Fp(\241)30710 30260
y Fo(1)p 30497 30421 833 40 v 30497 30969 a(2)p Fn(d)31518
31170 y Fu(e)32121 30622 y Fs(9)p Fq(q)33043 30216 y
Fm(\241)33815 29956 y Fo(1)p 33815 30067 406 33 v 33815
30526 a(2)34465 31170 y Fx(\))34971 30622 y Fs(2)45176
31170 y Fx(\(36\))4317 34629 y(pro)-36 b(vided)433 b
Fu(\271)10447 34828 y Fq(d)10986 34629 y Fu(g)48 b(q)12282
34139 y Fp(\241)13359 33777 y Fo(1)p 13146 33938 833
40 v 13146 34486 a(2)p Fn(d)14167 34629 y Fu(e)14770
34147 y Fs(9)p Fq(q)15692 33742 y Fm(\241)16464 33481
y Fo(1)p 16464 33592 406 33 v 16464 34052 a(2)17483 34629
y Fu(<)368 b Fx(1.)579 b(This)434 b(implies)14835 37525
y Fu(\302)15650 36977 y Fs(w)16398 37525 y Fx(\()p Fu(\257)17638
37724 y Fq(t)18033 37525 y Fu(;)221 b(q)48 b Fx(\))369
b(=)21496 36449 y Fj(\243)22049 37525 y Fx(\()p Fr(\241)p
Fx(1\))24744 36977 y Fq(d)p Fp(\241)p Fs(1)26486 37525
y Fu(d)27162 36449 y Fj(\244)27715 37525 y Fu(q)28340
36977 y Fp(\241)29215 36615 y Fo(1)p 29204 36776 427
40 v 29204 37324 a Fn(d)30115 37525 y Fx(+)294 b Fu(O)36
b Fx(\()p Fu(q)33582 36977 y Fp(\241)34457 36615 y Fo(1)p
34446 36776 V 34446 37324 a Fn(d)35006 36977 y Fp(\241)35871
36615 y Fo(1)p 35871 36776 406 40 v 35871 37324 a(2)36465
37525 y Fx(\))8205 b(\(37\))4317 40421 y(giving)344 b(the)e(second)g
(statemen)-36 b(t)341 b(of)i(the)f(theorem.)548 b(The)342
b(last)h(statemen)-36 b(t)341 b(follo)-36 b(ws)345 b(again)4317
42026 y(from)434 b(the)f(di\256eren)-36 b(tiabilit)g(y)434
b(prop)36 b(erties)433 b(giv)-36 b(en)434 b(in)g([LMMRS)o(].)p
36298 42026 651 651 v 6268 44223 a(Let)606 b(us)g(giv)-36
b(e)608 b(some)e(consequences)h(of)g(Theorem)g(6.)1097
b(Consider)606 b(a)h(generalized)4317 45828 y(F)-108
b(ortuin{Kasteleyn)556 b(measure)g(\(GFK\))f(where)h(the)f(o)36
b(ccupation)556 b(v)-72 b(ariables)557 b(are)f(de-)4317
47433 y(\257ned)433 b(on)g(the)g(\()p Fu(d)295 b Fr(\241)g
Fx(1\){cells)435 b(of)f(the)f(lattice:)7306 50921 y Fr(h)221
b(\242)g(i)p Fx(\()p Ft(V)p Fu(;)g(\257)74 b(;)221 b(q)48
b Fx(\))370 b(=)17995 50023 y(1)p 15602 50616 5436 54
v 15602 51833 a(\245\()p Ft(V)p Fu(;)221 b(\257)74 b(;)221
b(q)48 b Fx(\))22371 49660 y Fj(X)21392 52583 y Fq(n)p
Fp(2f)p Fs(0)p Fq(;)p Fs(1)p Fp(g)24731 52331 y Fc(V)25490
50921 y Fr(\242)221 b Fx(\()p Fu(e)27189 50373 y Fq(\257)28113
50921 y Fr(\241)296 b Fx(1\))30598 50373 y Fq(N)31439
50060 y Fn(d)p Fm(\241)p Fo(1)32966 50373 y Fs(\()p Fq(n)p
Fs(\))34324 50921 y Fu(q)34949 50373 y Fq(\274)35521
50060 y Fn(d)p Fm(\241)p Fo(1)37048 50373 y Fs(\()p Fq(n)p
Fs(\))38628 50921 y Fu(\267)39377 50373 y Fs(b)26 b(c)40399
50921 y Fx(\()p Fu(n)p Fx(\))2989 b(\(38\))4317 55436
y(where)416 b Ft(V)370 b Fr(\275)f Ft(L)11674 55635 y
Fq(d)p Fp(\241)p Fs(1)13831 55436 y Fx(and)416 b Fu(\267)17092
54954 y Fs(b)26 b(c)18114 55436 y Fx(\()p Fu(n)p Fx(\))416
b(refers)h(to)f(the)g(b)36 b(oundary)415 b(conditions.)573
b(In)416 b(dimension)4317 57041 y Fu(d)619 b Fx(=)g(3,)f(the)580
b(partition)h(function)f(\245\()p Ft(V)p Fu(;)221 b(\257)74
b(;)221 b(q)48 b Fx(\))582 b(is)f(actually)g(the)g(F)-108
b(ortuin{Kasteleyn)4317 58646 y(represen)-36 b(tation)488
b(of)h(the)f(gauge)i(P)-36 b(otts)488 b(mo)36 b(del.)744
b(In)488 b(dimension)h Fu(d)462 b Fr(\270)h Fx(4,)503
b(it)489 b(is)g(the)f(one)4317 60251 y(of)496 b(the)e(so{called)i(h)-36
b(yp)36 b(ergauge)495 b(mo)36 b(del.)762 b(P)-36 b(otts)495
b(and)f(h)-36 b(yp)36 b(ergauge)495 b(P)-36 b(otts)494
b(mo)36 b(del)495 b(are)4317 61856 y(related)571 b(b)-36
b(y)571 b(the)f(natural)h(extension)g(\()p Fb(D)p Fx(\))f(of)i(the)e
(Kramers-W)-108 b(annier)570 b(dualit)-36 b(y)-108 b(,)606
b(i.e.)4317 63461 y(F)-108 b(ourier)433 b(expansion)h(together)f(with)h
(P)-36 b(oincar)g(\266)-614 b(e)434 b(dualit)-36 b(y)434
b([LMeR,)g(KLMR)o(])17476 66694 y(P)-36 b(otts)21926
65941 y Fa(D)21091 66694 y Fr(\303)-221 b(!)590 b Fx(Hyp)36
b(ergauge)435 b(P)-36 b(otts)25253 70015 y(23)p eop
%%Page: 24 24
24 23 bop 4317 7306 a Fx(Denoting)348 b(b)-36 b(y)348
b(FK)g(and)f(GFK)h(their)f(F)-108 b(ortuin{Kasteleyn)348
b(represen)-36 b(tations,)364 b(the)348 b(com-)4317 8911
y(plete)434 b(comm)-36 b(utativit)g(y)434 b(of)g(the)f(follo)-36
b(wing)436 b(diagram)16960 12005 y(P)-36 b(otts)21926
11252 y Fa(D)21091 12005 y Fr(\303)-221 b(!)1107 b Fx(Hyp)36
b(ergauge)434 b(P)-36 b(otts)18029 12487 y Fj(?)18029
13284 y(?)18029 14081 y(y)29297 12487 y(?)29297 13284
y(?)29297 14081 y(y)17542 16378 y Fx(FK)21978 15625 y
Fa(A)21091 16378 y Fr(\303)-221 b(!)4773 b Fx(GFK)4317
19695 y(actually)471 b(holds.)685 b(The)470 b(corresp)36
b(ondence)468 b(FK)28318 18942 y Fa(A)27430 19695 y Fr(\303)-221
b(!)430 b Fx(GFK)469 b(is)h(the)f(Alexander)g(dualit)-36
b(y)4317 21301 y(\(used)433 b(in)g(Section)h(2)f(for)i
Fu(d)368 b Fx(=)h(2\))434 b(and)f(de\257ned)f(as)i(follo)-36
b(ws)19883 24131 y Fj(b)-758 b Fu(n)20639 24330 y Fq(b)21042
24078 y Fm(\244)21946 24131 y Fx(=)369 b(1)295 b Fr(\241)h
Fu(n)26377 24330 y Fq(b)26835 24131 y Fu(;)1522 b(b)369
b Fr(2)g Fu(V)4317 26962 y Fx(where)434 b Fu(b)8628 26480
y Fp(\244)9587 26962 y Fx(is)g(the)f(\()p Fu(d)295 b
Fr(\241)g Fx(1\){cell)435 b(that)e(crosses)h Fu(b)p Fx(.)6268
29150 y(Under)427 b(this)h(transformation,)i(the)d(FK)h(measure)g
(\(5\))g(at)g(\(in)-36 b(v)g(erse\))428 b(temp)36 b(erature)4317
30755 y Fu(\257)428 b Fx(is)355 b(transformed)f(in)g(the)g(GFK)g
(measure)g(\(38\))g(at)h(\(in)-36 b(v)g(erse\))354 b(temp)36
b(erature)353 b Fu(\257)43269 30273 y Fp(\244)43795 30755
y Fx(,)370 b(while)4317 32360 y(free)365 b(b)36 b(oundary)363
b(conditions)h(are)g(transformed)g(in)-36 b(to)364 b(the)g(wired)g
(ones.)555 b(Note)364 b(that)g(this)4317 33965 y(dualit)-36
b(y)454 b(actually)g(holds)f(at)g(the)g(lev)-36 b(el)454
b(of)g(measures.)637 b(It)453 b(implies,)459 b(as)453
b(a)h(consequence)4317 35570 y(of)597 b(Theorem)f(6,)636
b(that)596 b(the)f(\(suitably)h(de\257ned\))e(mean)i(lo)36
b(cal)597 b(Euler)e(c)-36 b(haracteristic)4317 37175
y(with)541 b(resp)36 b(ect)541 b(to)g(the)f(generalized)i(measures)f
(\(38\))g(is)g(discon)-36 b(tin)g(uous)540 b(at)h(the)g(dual)4317
38781 y(temp)36 b(erature)433 b Fu(\257)12532 38299 y
Fp(\244)12458 39109 y Fq(t)13491 38781 y Fx(giv)-36 b(en)434
b(b)-36 b(y)434 b(\()p Fu(e)19803 38299 y Fq(\257)20377
37986 y Fm(\244)20331 38554 y Fn(t)21206 38781 y Fr(\241)295
b Fx(1\)\()p Fu(e)24799 38299 y Fq(\257)25327 38410 y
Fn(t)26050 38781 y Fr(\241)g Fx(1\))369 b(=)g Fu(q)48
b Fx(.)4317 43786 y Fy(4)2152 b(Conclusion)716 b(and)g(outlo)60
b(oks)4317 47289 y Fx(This)651 b(w)-36 b(ork)652 b(clearly)g(sho)-36
b(ws)651 b(that)f(the)h(mean)f(Euler-P)-36 b(oincar)g(\266)-614
b(e)651 b(c)-36 b(haracteristic)651 b(p)36 b(er)4317
48894 y(site)613 b(of)h(the)f(FK)f(measure)h(exhibits)g(a)h
(non-trivial)f(b)36 b(eha)-36 b(viour)613 b(at)g(the)g(transition)4317
50499 y(p)36 b(oin)-36 b(t.)739 b(More)487 b(precisely)-108
b(,)502 b(w)-36 b(e)487 b(ha)-36 b(v)g(e)488 b(pro)-36
b(v)g(ed)487 b(that)f(it)i(satis\257es,)501 b(in)487
b(dimension)g(t)-36 b(w)g(o,)501 b(a)4317 52104 y(dualit)-36
b(y)480 b(prop)36 b(ert)-36 b(y)479 b(implying)h(that)f(at)g(the)g
(transition)h(p)36 b(oin)-36 b(t)479 b(it)g(is)h(either)f(zero)h(or)f
(it)4317 53709 y(is)434 b(discon)-36 b(tin)g(uous.)6268
55898 y(F)-108 b(or)449 b(the)f(p)36 b(ercolation)449
b(mo)36 b(del)449 b(\()p Fu(q)443 b Fx(=)394 b(1\))449
b(it)g(actually)h(tak)-36 b(es)449 b(the)g(v)-72 b(alue)449
b(zero)g(at)g(the)4317 57503 y(transition)434 b(p)36
b(oin)-36 b(t.)6268 59691 y(Moreo)g(v)g(er,)467 b(for)461
b(large)f Fu(q)48 b Fx(,)466 b(using)460 b(an)g(analysis)h(of)g(the)e
(order{disorder)g(transition,)4317 61296 y(w)-36 b(e)393
b(ha)-36 b(v)g(e)392 b(sho)-36 b(wn)392 b(that)g(a)h(jump)e(of)i(order)
f Fu(q)25610 60806 y Fp(\241)26475 60444 y Fo(1)p 26474
60605 406 40 v 26474 61153 a(2)27461 61296 y Fx(o)36
b(ccurs.)564 b(This)393 b(is)f(illustrated)h(in)f(Figure)4317
62901 y(2)434 b(for)g Fu(q)416 b Fx(=)369 b(5000.)6268
65089 y(In)403 b(higher)f(dimensions,)409 b(the)402 b(magnitude)h(of)g
(the)f(jump)h(is)g(of)g(order)g Fu(q)41122 64599 y Fp(\241)41997
64237 y Fo(1)p 41986 64398 427 40 v 41986 64946 a Fn(d)43003
65089 y Fx(for)h(ev)-36 b(en)4317 66694 y(space)434 b(dimensions)f(and)
g(of)h(order)g Fu(q)22487 66204 y Fp(\241)23352 65831
y Fn(d)p Fm(\241)p Fo(1)p 23351 66003 1473 40 v 23873
66551 a Fn(d)25445 66694 y Fx(for)g(o)36 b(dd)433 b(space)h
(dimensions.)25253 70015 y(24)p eop
%%Page: 25 25
25 24 bop 4317 25169 a @beginspecial -56 @llx 60 @lly
663 @urx 397 @ury 3685 @rwi @setspecial
%%BeginDocument: chi_n15000.eps
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: Adobe Illustrator(TM) 7.0
%%For: (--- - cpt) (cnrs)
%%Title: (chi_n15000.eps)
%%CreationDate: (12/16/02) (2:38 PM)
%%BoundingBox: -56 60 663 397
%%HiResBoundingBox: -55.7939 60.4021 662.565 396.7239
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%DocumentFonts: Times-Italic
%%DocumentNeededFonts: Times-Italic
%%DocumentSuppliedResources: procset Adobe_level2_AI5 1.2 0
%%+ procset Adobe_typography_AI5 1.0 1
%%+ procset Adobe_ColorImage_AI6 1.1 0
%%+ procset Adobe_Illustrator_AI5 1.2 0
%%+ procset Adobe_cshow 2.0 8
%AI5_FileFormat 3.0
%AI3_ColorUsage: Color
%AI3_IncludePlacedImages
%AI7_ImageSettings: 1
%%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set)
%%+ Options: 1 16 0 1 0 1 1 1 0 1 1 1 1 18 0 0 0 0 0 0 0 0 -1 -1
%%+ PPD: 1 21 0 0 60 45 2 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 ()
%AI3_TemplateBox: 300 225 300 225
%AI3_TileBox: -96.5 -54 700.5 506
%AI3_DocumentPreview: Macintosh_ColorPic
%AI5_ArtSize: 842 595
%AI5_RulerUnits: 2
%AI5_ArtFlags: 1 0 0 1 0 0 1 1 0
%AI5_TargetResolution: 800
%AI5_NumLayers: 1
%AI5_OpenToView: -156 489 -1 1146 725 18 0 1 3 40 0 0
%AI5_OpenViewLayers: 7
%%PageOrigin:-96.5 -54
%%AI3_PaperRect:-23 577 819 -18
%%AI3_Margin:23 -17 -22 18
%AI7_GridSettings: 72 8 72 8 1 0 0.8 0.8 0.8 0.9 0.9 0.9
%%EndComments
%%BeginProlog
%%BeginResource: procset Adobe_level2_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation)
%%Version: 1.2 0
%%CreationDate: (04/10/93) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
userdict /Adobe_level2_AI5 25 dict dup begin
	put
	/packedarray where not
	{
		userdict begin
		/packedarray
		{
			array astore readonly
		} bind def
		/setpacking /pop load def
		/currentpacking false def
	 end
		0
	} if
	pop
	userdict /defaultpacking currentpacking put true setpacking
	/initialize
	{
		Adobe_level2_AI5 begin
	} bind def
	/terminate
	{
		currentdict Adobe_level2_AI5 eq
		{
		 end
		} if
	} bind def
	mark
	/setcustomcolor where not
	{
		/findcmykcustomcolor
		{
			0
			6 packedarray
		} bind def
		/findrgbcustomcolor
		{
			1
			5 packedarray
		} bind def
		/setcustomcolor
		{
			exch
			aload pop
			0 eq
			{
				pop
				4
				{
					4 index mul
					4 1 roll
				} repeat
				5 -1 roll pop
				setcmykcolor
			}
			{
				pop
				3
				{
					1 exch sub
					3 index mul
					1 exch sub
					3 1 roll
				} repeat
				4 -1 roll pop
				setrgbcolor
			} ifelse
		}
		def
	} if

	/gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def
	userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put
	userdict /level2?
	systemdict /languagelevel known dup
	{
		pop systemdict /languagelevel get 2 ge
	} if
	put
/level2ScreenFreq
{
 begin
		60
		HalftoneType 1 eq
		{
			pop Frequency
		} if
		HalftoneType 2 eq
		{
			pop GrayFrequency
		} if
		HalftoneType 5 eq
		{
			pop Default level2ScreenFreq
		} if
 end
} bind def
userdict /currentScreenFreq
	level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put
level2? not
	{
		/setcmykcolor where not
		{
			/setcmykcolor
			{
				exch .11 mul add exch .59 mul add exch .3 mul add
				1 exch sub setgray
			} def
		} if
		/currentcmykcolor where not
		{
			/currentcmykcolor
			{
				0 0 0 1 currentgray sub
			} def
		} if
		/setoverprint where not
		{
			/setoverprint /pop load def
		} if
		/selectfont where not
		{
			/selectfont
			{
				exch findfont exch
				dup type /arraytype eq
				{
					makefont
				}
				{
					scalefont
				} ifelse
				setfont
			} bind def
		} if
		/cshow where not
		{
			/cshow
			{
				[
				0 0 5 -1 roll aload pop
				] cvx bind forall
			} bind def
		} if
	} if
	cleartomark
	/anyColor?
	{
		add add add 0 ne
	} bind def
	/testColor
	{
		gsave
		setcmykcolor currentcmykcolor
		grestore
	} bind def
	/testCMYKColorThrough
	{
		testColor anyColor?
	} bind def
	userdict /composite?
	level2?
	{
		gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore
		add add add 4 eq
	}
	{
		1 0 0 0 testCMYKColorThrough
		0 1 0 0 testCMYKColorThrough
		0 0 1 0 testCMYKColorThrough
		0 0 0 1 testCMYKColorThrough
		and and and
	} ifelse
	put
	composite? not
	{
		userdict begin
		gsave
		/cyan? 1 0 0 0 testCMYKColorThrough def
		/magenta? 0 1 0 0 testCMYKColorThrough def
		/yellow? 0 0 1 0 testCMYKColorThrough def
		/black? 0 0 0 1 testCMYKColorThrough def
		grestore
		/isCMYKSep? cyan? magenta? yellow? black? or or or def
		/customColor? isCMYKSep? not def
	 end
	} if
 end defaultpacking setpacking
%%EndResource
%%BeginResource: procset Adobe_typography_AI5 1.0 1
%%Title: (Typography Operators)
%%Version: 1.0 1
%%CreationDate:(6/10/1996) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_typography_AI5 68 dict dup begin
put
/initialize
{
 begin
 begin
	Adobe_typography_AI5 begin
	Adobe_typography_AI5
	{
		dup xcheck
		{
			bind
		} if
		pop pop
	} forall
 end
 end
 end
	Adobe_typography_AI5 begin
} def
/terminate
{
	currentdict Adobe_typography_AI5 eq
	{
	 end
	} if
} def
/modifyEncoding
{
	/_tempEncode exch ddef
	/_pntr 0 ddef
	{
		counttomark -1 roll
		dup type dup /marktype eq
		{
			pop pop exit
		}
		{
			/nametype eq
			{
				_tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll
				put
			}
			{
				/_pntr exch ddef
			} ifelse
		} ifelse
	} loop
	_tempEncode
} def
/havefont
{
	systemdict /languagelevel known
		{
		/Font resourcestatus dup
			{ exch pop exch pop }
		if
		}
		{
		systemdict /FontDirectory get 1 index known
			{ pop true }
			{
			systemdict /fileposition known
				{
				dup length 6 add exch
				Ss 6 250 getinterval
				cvs pop
				Ss exch 0 exch getinterval
				status
					{ pop pop pop pop true }
					{ false }
				ifelse
				}
				{
				pop false
				}
			ifelse
			}
		ifelse
		}
	ifelse
} def
/TE
{
	StandardEncoding 256 array copy modifyEncoding
	/_nativeEncoding exch def
} def
/subststring {
	exch 2 index exch search
	{
		exch pop
		exch dup () eq
		{
			pop exch concatstring
		}
		{
			3 -1 roll
			exch concatstring
			concatstring
		} ifelse
		exch pop true
	}
	{
		pop pop false
	} ifelse
} def
/concatstring {
	1 index length 1 index length
	1 index add
	string
	dup 0 5 index putinterval
	dup 2 index 4 index putinterval
	4 1 roll pop pop pop
} def
%
/TZ
{
	dup type /arraytype eq
	{
		/_wv exch def
	}
	{
		/_wv 0 def
	} ifelse
	/_useNativeEncoding exch def
	2 index havefont
	{
		3 index
		255 string
		cvs

		dup
		(_Symbol_)
		eq
		{
			pop
			2 index
			findfont

		}
		{
			dup length 1 sub
			1 exch
			getinterval

			cvn
			findfont
		} ifelse
	}
	{
		dup 1 eq
		{
			2 index 64 string cvs
			dup (-90pv-RKSJ-) (-83pv-RKSJ-) subststring
			{
				exch pop dup havefont
				{
					findfont false
				}
				{
					pop true
				} ifelse
			}
			{
				pop	dup
				(-90ms-RKSJ-) (-Ext-RKSJ-) subststring
				{
					exch pop dup havefont
					{
						findfont false
					}
					{
						pop true
					} ifelse
				}
				{
					pop pop true
				} ifelse
			} ifelse
			{
				/Ryumin-Light-83pv-RKSJ-H havefont
					{/Ryumin-Light-83pv-RKSJ-H}
					{/Courier}
					ifelse
					findfont
					[1 0 0.5 1 0 0] makefont
			} if
		}
		{
			/Courier findfont
		} ifelse
	} ifelse
	_wv type /arraytype eq
	{
		_wv makeblendedfont
	} if
	dup length 10 add dict
 begin
	mark exch
	{
		1 index /FID ne
		{
			def
		} if
		cleartomark mark
	} forall
	pop
	/FontScript exch def
	/FontDirection exch def
	/FontRequest exch def
	/FontName exch def
	counttomark 0 eq
	{
		1 _useNativeEncoding eq
		{
			/Encoding _nativeEncoding def
		} if
		cleartomark
	}
	{
		/Encoding load 256 array copy
		modifyEncoding /Encoding exch def
	} ifelse
	FontName currentdict
 end
	definefont pop
} def
/tr
{
	_ax _ay 3 2 roll
} def
/trj
{
	_cx _cy _sp _ax _ay 6 5 roll
} def
/a0
{
	/Tx
	{
		dup
		currentpoint 3 2 roll
		tr _psf
		newpath moveto
		tr _ctm _pss
	} ddef
	/Tj
	{
		dup
		currentpoint 3 2 roll
		trj _pjsf
		newpath moveto
		trj _ctm _pjss
	} ddef
} def
/a1
{
W B
} def
/e0
{
	/Tx
	{
		tr _psf
	} ddef
	/Tj
	{
		trj _pjsf
	} ddef
} def
/e1
{
W F
} def
/i0
{
	/Tx
	{
		tr sp
	} ddef
	/Tj
	{
		trj jsp
	} ddef
} def
/i1
{
	W N
} def
/o0
{
	/Tx
	{
		tr sw rmoveto
	} ddef
	/Tj
	{
		trj swj rmoveto
	} ddef
} def
/r0
{
	/Tx
	{
		tr _ctm _pss
	} ddef
	/Tj
	{
		trj _ctm _pjss
	} ddef
} def
/r1
{
W S
} def
/To
{
	pop _ctm currentmatrix pop
} def
/TO
{
	iTe _ctm setmatrix newpath
} def
/Tp
{
	pop _tm astore pop _ctm setmatrix
	_tDict begin
	/W
	{
	} def
	/h
	{
	} def
} def
/TP
{
 end
	iTm 0 0 moveto
} def
/Tr
{
	_render 3 le
	{
		currentpoint newpath moveto
	} if
	dup 8 eq
	{
		pop 0
	}
	{
		dup 9 eq
		{
			pop 1
		} if
	} ifelse
	dup /_render exch ddef
	_renderStart exch get load exec
} def
/iTm
{
	_ctm setmatrix _tm concat
	_shift aload pop _lineorientation 1 eq { exch } if translate
	_scale aload pop _lineorientation 1 eq _yokoorientation 1 eq or { exch } if scale
} def
/Tm
{
	_tm astore pop iTm 0 0 moveto
} def
/Td
{
	_mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto
} def
/iTe
{
	_render -1 eq
	{
	}
	{
		_renderEnd _render get dup null ne
		{
			load exec
		}
		{
			pop
		} ifelse
	} ifelse
	/_render -1 ddef
} def
/Ta
{
	pop
} def
/Tf
{
	1 index type /nametype eq
	{
		dup 0.75 mul 1 index 0.25 mul neg
	} if
	/_fontDescent exch ddef
	/_fontAscent exch ddef
	/_fontSize exch ddef
	/_fontRotateAdjust _fontAscent _fontDescent add 2 div neg ddef
	/_fontHeight _fontSize ddef
	findfont _fontSize scalefont setfont
} def
/Tl
{
	pop neg 0 exch
	_leading astore pop
} def
/Tt
{
	pop
} def
/TW
{
	3 npop
} def
/Tw
{
	/_cx exch ddef
} def
/TC
{
	3 npop
} def
/Tc
{
	/_ax exch ddef
} def
/Ts
{
	0 exch
	_shift astore pop
	currentpoint
	iTm
	moveto
} def
/Ti
{
	3 npop
} def
/Tz
{
	count 1 eq { 100 } if
	100 div exch 100 div exch
	_scale astore pop
	iTm
} def
/TA
{
	pop
} def
/Tq
{
	pop
} def
/Tg
{
	pop
} def
/TG
{
	pop
} def
/Tv
{
	/_lineorientation exch ddef
} def
/TV
{
	/_charorientation exch ddef
} def
/Ty
{
	dup /_yokoorientation exch ddef 1 sub neg Tv
} def
/TY
{
	pop
} def
/T~
{
	Tx
} def
/Th
{
	pop pop pop pop pop
} def
/TX
{
	pop
} def
/Tk
{
	_fontSize mul 1000 div
	_lineorientation 0 eq { neg 0 } { 0 exch } ifelse
	rmoveto
	pop
} def
/TK
{
	2 npop
} def
/T*
{
	_leading aload pop
	_lineorientation 0 ne { exch } if
	Td
} def
/T*-
{
	_leading aload pop
	_lineorientation 0 ne { exch } if
	exch neg exch neg
	Td
} def
/T-
{
	_ax neg 0 rmoveto
	_lineorientation 1 eq _charorientation 0 eq and { 1 TV _hyphen Tx 0 TV } { _hyphen Tx } ifelse
} def
/T+
{
} def
/TR
{
	_ctm currentmatrix pop
	_tm astore pop
	iTm 0 0 moveto
} def
/TS
{
	currentfont 3 1 roll
	/_Symbol_ findfont _fontSize scalefont setfont

	0 eq
	{
		Tx
	}
	{
		Tj
	} ifelse
	setfont
} def
/Xb
{
	pop pop
} def
/Tb /Xb load def
/Xe
{
	pop pop pop pop
} def
/Te /Xe load def
/XB
{
} def
/TB /XB load def
currentdict readonly pop
end
setpacking
%
/X^
{
	currentfont 5 1 roll
	dup havefont
		{
		findfont _fontSize scalefont setfont
		}
		{
		pop
		exch
		} ifelse
	2 index 0 eq
	{
		Tx
	}
	{
		Tj
	} ifelse
	pop	pop
	setfont
} def
/T^	/X^	load def
%%EndResource
%%BeginProcSet: Adobe_ColorImage_AI6 1.1 0
userdict /Adobe_ColorImage_AI6 known not
{
	userdict /Adobe_ColorImage_AI6 24 dict put
} if
userdict /Adobe_ColorImage_AI6 get begin
/initialize
{
	Adobe_ColorImage_AI6 begin
	Adobe_ColorImage_AI6
	{
		dup type /arraytype eq
		{
			dup xcheck
			{
				bind
			} if
		} if
		pop pop
	} forall
} def
/terminate { end } def
currentdict /Adobe_ColorImage_AI6_Vars known not
{
	/Adobe_ColorImage_AI6_Vars 15 dict def
} if
Adobe_ColorImage_AI6_Vars begin
	/channelcount 0 def
	/sourcecount 0 def
	/sourcearray 4 array def
	/plateindex -1 def
	/XIMask 0 def
	/XIBinary 0 def
	/XIChannelCount 0 def
	/XIBitsPerPixel 0 def
	/XIImageHeight 0 def
	/XIImageWidth 0 def
	/XIImageMatrix null def
	/XIBuffer null def
	/XIDataProc null def
	/XIVersion 6 def
end
/WalkRGBString null def
/WalkCMYKString null def
/StuffRGBIntoGrayString null def
/RGBToGrayImageProc null def
/StuffCMYKIntoGrayString null def
/CMYKToGrayImageProc null def
/ColorImageCompositeEmulator null def
/SeparateCMYKImageProc null def
/FourEqual null def
/TestPlateIndex null def
currentdict /_colorimage known not
{
	/colorimage where
	{
		/colorimage get /_colorimage exch def
	}
	{
		/_colorimage null def
	} ifelse
} if
/_currenttransfer systemdict /currenttransfer get def
/colorimage null def
/XI null def
/WalkRGBString
{
	0 3 index
	dup length 1 sub 0 3 3 -1 roll
	{
		3 getinterval { } forall
		5 index exec
		3 index
	} for

	 5 { pop } repeat
} def
/WalkCMYKString
{
	0 3 index
	dup length 1 sub 0 4 3 -1 roll
	{
		4 getinterval { } forall

		6 index exec

		3 index

	} for

	5 { pop } repeat

} def
/StuffRGBIntoGrayString
{
	.11 mul exch

	.59 mul add exch

	.3 mul add

	cvi 3 copy put

	pop 1 add
} def
/RGBToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 3 idiv string
		dup 3 1 roll

		/StuffRGBIntoGrayString load exch
		WalkRGBString
 end
} def
/StuffCMYKIntoGrayString
{
	exch .11 mul add

	exch .59 mul add

	exch .3 mul add

	dup 255 gt { pop 255 } if

	255 exch sub cvi 3 copy put

	pop 1 add
} def
/CMYKToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 4 idiv string
		dup 3 1 roll

		/StuffCMYKIntoGrayString load exch
		WalkCMYKString
 end
} def
/ColorImageCompositeEmulator
{
	pop true eq
	{
		Adobe_ColorImage_AI6_Vars /sourcecount get 5 add { pop } repeat
	}
	{
		Adobe_ColorImage_AI6_Vars /channelcount get 1 ne
		{
			Adobe_ColorImage_AI6_Vars begin
				sourcearray 0 3 -1 roll put

				channelcount 3 eq
				{
					/RGBToGrayImageProc
				}
				{
					/CMYKToGrayImageProc
				} ifelse
				load
		 end
		} if
		image
	} ifelse
} def
/SeparateCMYKImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcecount 0 ne
		{
			sourcearray plateindex get exec
		}
		{
			sourcearray 0 get exec

			dup length 4 idiv string

			0 2 index

			plateindex 4 2 index length 1 sub
			{
				get 255 exch sub

				3 copy put pop 1 add

				2 index
			} for
			pop pop exch pop
		} ifelse
 end
} def

/FourEqual
{
	4 index ne
	{
		pop pop pop false
	}
	{
		4 index ne
		{
			pop pop false
		}
		{
			4 index ne
			{
				pop false
			}
			{
				4 index eq
			} ifelse
		} ifelse
	} ifelse
} def
/TestPlateIndex
{
	Adobe_ColorImage_AI6_Vars begin
		/plateindex -1 def
		/setcmykcolor where
		{
			pop
			gsave
			1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
			grestore
			1 0 0 0 FourEqual
			{
				/plateindex 0 def
			}
			{
				0 1 0 0 FourEqual
				{
					/plateindex 1 def
				}
				{
					0 0 1 0 FourEqual
					{
						/plateindex 2 def
					}
					{
						0 0 0 1 FourEqual
						{
							/plateindex 3 def
						}
						{
							0 0 0 0 FourEqual
							{
								/plateindex 5 def
							} if
						} ifelse
					} ifelse
				} ifelse
			} ifelse
			pop pop pop pop
		} if
		plateindex
 end
} def
/colorimage
{
	Adobe_ColorImage_AI6_Vars begin
		/channelcount 1 index def
		/sourcecount 2 index 1 eq { channelcount 1 sub } { 0 } ifelse def
		4 sourcecount add index dup
		8 eq exch 1 eq or not
 end

	{
		/_colorimage load null ne
		{
			_colorimage
		}
		{
			Adobe_ColorImage_AI6_Vars /sourcecount get
			7 add { pop } repeat
		} ifelse
	}
	{
		dup 3 eq
		TestPlateIndex
		dup -1 eq exch 5 eq or or
		{
			/_colorimage load null eq
			{
				ColorImageCompositeEmulator
			}
			{
				dup 1 eq
				{
					pop pop image
				}
				{
					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						gsave

						0 _currenttransfer exec
						1 _currenttransfer exec
						eq
						{ 0 _currenttransfer exec 0.5 lt }
						{ 0 _currenttransfer exec 1 _currenttransfer exec gt } ifelse

						{ { pop 0 } } { { pop 1 } } ifelse
						systemdict /settransfer get exec
					} if

					_colorimage

					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						grestore
					} if
				} ifelse
			} ifelse
		}
		{
			dup 1 eq
			{
				pop pop
				image
			}
			{
				pop pop
				Adobe_ColorImage_AI6_Vars begin
					sourcecount -1 0
					{
						exch sourcearray 3 1 roll put
					} for
					/SeparateCMYKImageProc load
			 end
				systemdict /image get exec
			} ifelse
		} ifelse
	} ifelse
} def
/XG
{
	pop pop
} def
/XF
{
	13 {pop} repeat
} def
/Xh
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIImageHeight exch def
		/XIImageWidth exch def
		/XIImageMatrix exch def
		0 0 moveto
		XIImageMatrix concat
		XIImageWidth XIImageHeight scale

		XIMask
		{
			/_lp /null ddef
			_fc
			/_lp /imagemask ddef
		}
		if
		/XIVersion 7 def
 end
} def
/XH
{
	Adobe_ColorImage_AI6_Vars begin
		/XIVersion 6 def
		grestore
 end
} def
/XI
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIBinary exch 0 ne def
		pop
		pop
		/XIChannelCount exch def
		/XIBitsPerPixel exch def
		/XIImageHeight exch def
		/XIImageWidth exch def
		pop pop pop pop
		/XIImageMatrix exch def
		XIBitsPerPixel 1 eq
		{
			XIImageWidth 8 div ceiling cvi
		}
		{
			XIImageWidth XIChannelCount mul
		} ifelse
		/XIBuffer exch string def
		XIBinary
		{
			/XIDataProc { currentfile XIBuffer readstring pop } def
			XIVersion 6 le
			{
				currentfile 128 string readline pop pop
			}
			if
		}
		{
			/XIDataProc { currentfile XIBuffer readhexstring pop } def
		} ifelse

		XIVersion 6 le
		{
			0 0 moveto
			XIImageMatrix concat
			XIImageWidth XIImageHeight scale
			XIMask
			{
				/_lp /null ddef
				_fc
				/_lp /imagemask ddef
			} if
		} if

		XIMask
		{
			XIImageWidth XIImageHeight
			false
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load
			imagemask
		}
		{
			XIImageWidth XIImageHeight
			XIBitsPerPixel
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load

			XIChannelCount 1 eq
			{
				gsave
				0 setgray
				image
				grestore
			}
			{
				false
				XIChannelCount
				colorimage
			} ifelse
		} ifelse
		grestore
 end
} def
end
%%EndProcSet
%%BeginResource: procset Adobe_Illustrator_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 7.0 Full Prolog)
%%Version: 1.2 0
%%CreationDate: (3/7/1994) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_Illustrator_AI5_vars 107 dict dup begin
put
/_eo false def
/_lp /none def
/_pf
{
} def
/_ps
{
} def
/_psf
{
} def
/_pss
{
} def
/_pjsf
{
} def
/_pjss
{
} def
/_pola 0 def
/_doClip 0 def
/cf currentflat def
/_lineorientation 0 def
/_charorientation 0 def
/_yokoorientation 0 def
/_tm matrix def
/_renderStart
[
/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0
] def
/_renderEnd
[
null null null null /i1 /i1 /i1 /i1
] def
/_render -1 def
/_shift [0 0] def
/_ax 0 def
/_ay 0 def
/_cx 0 def
/_cy 0 def
/_leading
[
0 0
] def
/_ctm matrix def
/_mtx matrix def
/_sp 16#020 def
/_hyphen (-) def
/_fontSize 0 def
/_fontAscent 0 def
/_fontDescent 0 def
/_fontHeight 0 def
/_fontRotateAdjust 0 def
/Ss 256 string def
Ss 0 (fonts/) putinterval
/_cnt 0 def
/_scale [1 1] def
/_nativeEncoding 0 def
/_useNativeEncoding 0 def
/_tempEncode 0 def
/_pntr 0 def
/_tDict 2 dict def
/_hfname 100 string def
/_hffound false def
/Tx
{
} def
/Tj
{
} def
/CRender
{
} def
/_AI3_savepage
{
} def
/_gf null def
/_cf 4 array def
/_rgbf 3 array def
/_if null def
/_of false def
/_fc
{
} def
/_gs null def
/_cs 4 array def
/_rgbs 3 array def
/_is null def
/_os false def
/_sc
{
} def
/_pd 1 dict def
/_ed 15 dict def
/_pm matrix def
/_fm null def
/_fd null def
/_fdd null def
/_sm null def
/_sd null def
/_sdd null def
/_i null def
/_lobyte 0 def
/_hibyte 0 def
/_cproc null def
/_cscript 0 def
/_hvax 0 def
/_hvay 0 def
/_hvwb 0 def
/_hvcx 0 def
/_hvcy 0 def
/_bitfont null def
/_bitlobyte 0 def
/_bithibyte 0 def
/_bitkey null def
/_bitdata null def
/_bitindex 0 def
/discardSave null def
/buffer 256 string def
/beginString null def
/endString null def
/endStringLength null def
/layerCnt 1 def
/layerCount 1 def
/perCent (%) 0 get def
/perCentSeen? false def
/newBuff null def
/newBuffButFirst null def
/newBuffLast null def
/clipForward? false def
end
userdict /Adobe_Illustrator_AI5 known not {
	userdict /Adobe_Illustrator_AI5 95 dict put
} if
userdict /Adobe_Illustrator_AI5 get begin
/initialize
{
	Adobe_Illustrator_AI5 dup begin
	Adobe_Illustrator_AI5_vars begin
	discardDict
	{
		bind pop pop
	} forall
	dup /nc get begin
	{
		dup xcheck 1 index type /operatortype ne and
		{
			bind
		} if
		pop pop
	} forall
 end
	newpath
} def
/terminate
{
 end
 end
} def
/_
null def
/ddef
{
	Adobe_Illustrator_AI5_vars 3 1 roll put
} def
/xput
{
	dup load dup length exch maxlength eq
	{
		dup dup load dup
		length 2 mul dict copy def
	} if
	load begin
	def
 end
} def
/npop
{
	{
		pop
	} repeat
} def
/hswj
{
	dup stringwidth 3 2 roll
	{
		_hvwb eq { exch _hvcx add exch _hvcy add } if
		exch _hvax add exch _hvay add
	} cforall
} def
/vswj
{
	0 0 3 -1 roll
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			dup cstring stringwidth 5 2 roll
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			4 -1 roll sub exch
			3 -1 roll sub exch
		}
		{
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			_fontHeight sub
		} ifelse
	} cforall
} def
/swj
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hswj } { vswj } ifelse
} def
/sw
{
	0 0 0 6 3 roll swj
} def
/vjss
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			gsave
			false charpath currentpoint
			5 index setmatrix stroke
			grestore
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			gsave
			2 index false charpath
			6 index setmatrix stroke
			grestore

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjss
{
	4 1 roll
	{
		dup cstring
		gsave
		false charpath currentpoint
		5 index setmatrix stroke
		grestore
		moveto
		_sp eq
		{
			5 index 5 index rmoveto
		} if
		2 copy rmoveto
	} cforall
	6 npop
} def
/jss
{
	_lineorientation 0 eq { hjss } { vjss } ifelse
} def
/ss
{
	0 0 0 7 3 roll jss
} def
/vjsp
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			false charpath
            currentpoint
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			2 index false charpath

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjsp
{
    4 1 roll
    {
        dup cstring
        false charpath
        _sp eq
        {
            5 index 5 index rmoveto
        } if
        2 copy rmoveto
    } cforall
    6 npop
} def
/jsp
{
	matrix currentmatrix
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/sp
{
    matrix currentmatrix
    0 0 0 7 3 roll
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/pl
{
	transform
	0.25 sub round 0.25 add exch
	0.25 sub round 0.25 add exch
	itransform
} def
/setstrokeadjust where
{
	pop true setstrokeadjust
	/c
	{
		curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll curveto
	} def
	/V
	/v load def
	/y
	{
		2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		lineto
	} def
	/L
	/l load def
	/m
	{
		moveto
	} def
}
{
	/c
	{
		pl curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll pl curveto
	} def
	/V
	/v load def
	/y
	{
		pl 2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		pl lineto
	} def
	/L
	/l load def
	/m
	{
		pl moveto
	} def
} ifelse
/d
{
	setdash
} def
/cf
{
} def
/i
{
	dup 0 eq
	{
		pop cf
	} if
	setflat
} def
/j
{
	setlinejoin
} def
/J
{
	setlinecap
} def
/M
{
	setmiterlimit
} def
/w
{
	setlinewidth
} def
/XR
{
	0 ne
	/_eo exch ddef
} def
/H
{
} def
/h
{
	closepath
} def
/N
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			_eo {eoclip} {clip} ifelse /_doClip 0 ddef
		} if
		newpath
	}
	{
		/CRender
		{
			N
		} ddef
	} ifelse
} def
/n
{
	N
} def
/F
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc
			/_doClip 0 ddef
		}
		{
			_pf
		} ifelse
	}
	{
		/CRender
		{
			F
		} ddef
	} ifelse
} def
/f
{
	closepath
	F
} def
/S
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			_ps
		} ifelse
	}
	{
		/CRender
		{
			S
		} ddef
	} ifelse
} def
/s
{
	closepath
	S
} def
/B
{
	_pola 0 eq
	{
		_doClip 1 eq
		gsave F grestore
		{
			gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			S
		} ifelse
	}
	{
		/CRender
		{
			B
		} ddef
	} ifelse
} def
/b
{
	closepath
	B
} def
/W
{
	/_doClip 1 ddef
} def
/*
{
	count 0 ne
	{
		dup type /stringtype eq
		{
			pop
		} if
	} if
	newpath
} def
/u
{
} def
/U
{
} def
/q
{
	_pola 0 eq
	{
		gsave
	} if
} def
/Q
{
	_pola 0 eq
	{
		grestore
	} if
} def
/*u
{
	_pola 1 add /_pola exch ddef
} def
/*U
{
	_pola 1 sub /_pola exch ddef
	_pola 0 eq
	{
		CRender
	} if
} def
/D
{
	pop
} def
/*w
{
} def
/*W
{
} def
/`
{
	/_i save ddef
	clipForward?
	{
		nulldevice
	} if
	6 1 roll 4 npop
	concat pop
	userdict begin
	/showpage
	{
	} def
	0 setgray
	0 setlinecap
	1 setlinewidth
	0 setlinejoin
	10 setmiterlimit
	[] 0 setdash
	/setstrokeadjust where {pop false setstrokeadjust} if
	newpath
	0 setgray
	false setoverprint
} def
/~
{
 end
	_i restore
} def
/O
{
	0 ne
	/_of exch ddef
	/_lp /none ddef
} def
/R
{
	0 ne
	/_os exch ddef
	/_lp /none ddef
} def
/g
{
	/_gf exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_gf setgray
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/G
{
	/_gs exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_gs setgray
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/k
{
	_cf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_cf aload pop setcmykcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/K
{
	_cs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_cs aload pop setcmykcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/Xa
{
	_rgbf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_rgbf aload pop setrgbcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XA
{
	_rgbs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_rgbs aload pop setrgbcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/_rgbtocmyk
{
3
	{
	1 exch sub 3 1 roll
	} repeat
3 copy 1 4 1 roll
3
	{
	3 index 2 copy gt
		{
		exch
		} if
	pop 4 1 roll
	} repeat
pop pop pop
4 1 roll
3
	{
	3 index sub
	3 1 roll
	} repeat
4 -1 roll
} def
/Xx
{
	exch
	/_gf exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XX
{
	exch
	/_gs exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/x
{
	/_gf exch ddef
	findcmykcustomcolor
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/X
{
	/_gs exch ddef
	findcmykcustomcolor
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/A
{
	pop
} def
/annotatepage
{
userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse
} def
/XT {
	pop pop
} def
/discard
{
	save /discardSave exch store
	discardDict begin
	/endString exch store
	gt38?
	{
		2 add
	} if
	load
	stopped
	pop
 end
	discardSave restore
} bind def
userdict /discardDict 7 dict dup begin
put
/pre38Initialize
{
	/endStringLength endString length store
	/newBuff buffer 0 endStringLength getinterval store
	/newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store
	/newBuffLast newBuff endStringLength 1 sub 1 getinterval store
} def
/shiftBuffer
{
	newBuff 0 newBuffButFirst putinterval
	newBuffLast 0
	currentfile read not
	{
	stop
	} if
	put
} def
0
{
	pre38Initialize
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff endString eq
			{
				cleartomark stop
			} if
			shiftBuffer
		} loop
	}
	{
	stop
	} ifelse
} def
1
{
	pre38Initialize
	/beginString exch store
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff beginString eq
			{
				/layerCount dup load 1 add store
			}
			{
				newBuff endString eq
				{
					/layerCount dup load 1 sub store
					layerCount 0 eq
					{
						cleartomark stop
					} if
				} if
			} ifelse
			shiftBuffer
		} loop
	} if
} def
2
{
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		endString eq
		{
			cleartomark stop
		} if
	} loop
} def
3
{
	/beginString exch store
	/layerCnt 1 store
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		dup beginString eq
		{
			pop /layerCnt dup load 1 add store
		}
		{
			endString eq
			{
				layerCnt 1 eq
				{
					cleartomark stop
				}
				{
					/layerCnt dup load 1 sub store
				} ifelse
			} if
		} ifelse
	} loop
} def
end
userdict /clipRenderOff 15 dict dup begin
put
{
	/n /N /s /S /f /F /b /B
}
{
	{
		_doClip 1 eq
		{
			/_doClip 0 ddef _eo {eoclip} {clip} ifelse
		} if
		newpath
	} def
} forall
/Tr /pop load def
/Bb {} def
/BB /pop load def
/Bg {12 npop} def
/Bm {6 npop} def
/Bc /Bm load def
/Bh {4 npop} def
end
/Lb
{
	4 npop
	6 1 roll
	pop
	4 1 roll
	pop pop pop
	0 eq
	{
		0 eq
		{
			(%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard
		}
		{

			/clipForward? true def

			/Tx /pop load def
			/Tj /pop load def

			currentdict end clipRenderOff begin begin
		} ifelse
	}
	{
		0 eq
		{
			save /discardSave exch store
		} if
	} ifelse
} bind def
/LB
{
	discardSave dup null ne
	{
		restore
	}
	{
		pop
		clipForward?
		{
			currentdict
		 end
		 end
		 begin

			/clipForward? false ddef
		} if
	} ifelse
} bind def
/Pb
{
	pop pop
	0 (%AI5_EndPalette) discard
} bind def
/Np
{
	0 (%AI5_End_NonPrinting--) discard
} bind def
/Ln /pop load def
/Ap
/pop load def
/Ar
{
	72 exch div
	0 dtransform dup mul exch dup mul add sqrt
	dup 1 lt
	{
		pop 1
	} if
	setflat
} def
/Mb
{
	q
} def
/Md
{
} def
/MB
{
	Q
} def
/nc 4 dict def
nc begin
/setgray
{
	pop
} bind def
/setcmykcolor
{
	4 npop
} bind def
/setrgbcolor
{
	3 npop
} bind def
/setcustomcolor
{
	2 npop
} bind def
currentdict readonly pop
end
end
setpacking
%%EndResource
%%BeginResource: procset Adobe_cshow 2.0 8
%%Title: (Writing System Operators)
%%Version: 2.0 8
%%CreationDate: (1/23/89) ()
%%Copyright: ((C) 1992-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_cshow 14 dict dup begin put
/initialize
{
	Adobe_cshow begin
	Adobe_cshow
	{
		dup xcheck
		{
			bind
		} if
		pop pop
	} forall
 end
	Adobe_cshow begin
} def
/terminate
{
currentdict Adobe_cshow eq
	{
 end
	} if
} def
/cforall
{
	/_lobyte 0 ddef
	/_hibyte 0 ddef
	/_cproc exch ddef
	/_cscript currentfont /FontScript known { currentfont /FontScript get } { -1 } ifelse ddef
	{
		/_lobyte exch ddef
		_hibyte 0 eq
		_cscript 1 eq
		_lobyte 129 ge _lobyte 159 le and
		_lobyte 224 ge _lobyte 252 le and or and
		_cscript 2 eq
		_lobyte 161 ge _lobyte 254 le and and
		_cscript 3 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript 25 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript -1 eq
		or or or or and
		{
			/_hibyte _lobyte ddef
		}
		{
			_hibyte 256 mul _lobyte add
			_cproc
			/_hibyte 0 ddef
		} ifelse
	} forall
} def
/cstring
{
	dup 256 lt
	{
		(s) dup 0 4 3 roll put
	}
	{
		dup 256 idiv exch 256 mod
		(hl) dup dup 0 6 5 roll put 1 4 3 roll put
	} ifelse
} def
/clength
{
	0 exch
	{ 256 lt { 1 } { 2 } ifelse add } cforall
} def
/hawidthshow
{
	{
		dup cstring
		show
		_hvax _hvay rmoveto
		_hvwb eq { _hvcx _hvcy rmoveto } if
	} cforall
} def
/vawidthshow
{
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			-90 rotate
			0 _fontRotateAdjust rmoveto
			cstring
			_hvcx _hvcy _hvwb _hvax _hvay 6 -1 roll awidthshow
			0 _fontRotateAdjust neg rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			exch _hvay sub exch _hvax sub
			2 index _hvwb eq { exch _hvcy sub exch _hvcx sub } if
			3 2 roll
			cstring
			dup stringwidth pop 2 div neg _fontAscent neg rmoveto
			show
			moveto
		} ifelse
	} cforall
} def
/hvawidthshow
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hawidthshow } { vawidthshow } ifelse
} def
/hvwidthshow
{
	0 0 3 -1 roll hvawidthshow
} def
/hvashow
{
	0 0 0 6 -3 roll hvawidthshow
} def
/hvshow
{
	0 0 0 0 0 6 -1 roll hvawidthshow
} def
currentdict readonly pop end
setpacking
%%EndResource
%%EndProlog
%%BeginSetup
%%IncludeFont: Times-Italic
Adobe_level2_AI5 /initialize get exec
Adobe_cshow /initialize get exec
Adobe_Illustrator_AI5_vars Adobe_Illustrator_AI5 Adobe_typography_AI5 /initialize get exec
Adobe_ColorImage_AI6 /initialize get exec
Adobe_Illustrator_AI5 /initialize get exec
[
39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis
/Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute
/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde
/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex
/udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef
/guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide
/.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright
/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand
/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex
/Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex
/Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla
/hungarumlaut/ogonek/caron
TE
%AI55J_Tsume: None
%AI3_BeginEncoding: _Times-Italic Times-Italic
[/_Times-Italic/Times-Italic 0 0 1 TZ
%AI3_EndEncoding AdobeType
[161/degree 173/notequal 176/infinity/plusminus/lessequal/greaterequal
181/mu/partialdiff/summation/product/pi/integral 189/Omega
195/radical 197/approxequal 198/Delta 214/divide/lozenge 240/apple
/_Symbol_/Symbol 0 0 0 TZ
%AI5_Begin_NonPrinting
Np
%AI3_BeginPattern: (Acailles)
(Acailles) 1.6 9.3475 48.088 55.8355 [
%AI3_Tile
(0 O 0 R  1 g
 1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 9.3475 m
1.6 55.8355 L
48.088 55.8355 L
48.088 9.3475 L
1.6 9.3475 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R  0 g
 0 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
17.0956 9.3475 m
12.8162 9.3475 9.3475 5.8787 9.3475 1.6 C
9.3475 5.8787 5.8787 9.3475 1.6 9.3475 C
1.6 13.6262 5.0687 17.095 9.3475 17.095 c
13.6268 17.095 17.0956 13.6262 17.0956 9.3475 C
s
32.5918 9.3475 m
28.3125 9.3475 24.8437 5.8787 24.8437 1.6 C
24.8437 5.8787 21.3743 9.3475 17.0956 9.3475 C
17.0956 13.6262 20.5644 17.095 24.8437 17.095 c
29.1224 17.095 32.5918 13.6262 32.5918 9.3475 C
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48.088 9.3475 m
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(Bandes transparentes) Pc
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360.315 82.978 m
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427.215 84.078 m
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498.015 86.378 m
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500.115 86.578 m
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501.115 86.578 m
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502.115 86.578 m
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504.115 86.678 m
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506.215 86.778 m
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507.215 86.878 l
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508.215 86.878 m
508.215 86.878 l
S
509.315 87.178 m
510.315 86.178 l
511.315 87.178 l
510.315 88.178 l
509.315 87.178 l
S
510.315 87.178 m
510.315 87.178 l
S
511.315 379.578 m
512.315 378.578 l
513.315 379.578 l
512.315 380.578 l
511.315 379.578 l
S
512.315 379.578 m
512.315 379.578 l
S
513.415 379.678 m
514.415 378.678 l
515.415 379.678 l
514.415 380.678 l
513.415 379.678 l
S
514.415 379.678 m
514.415 379.678 l
S
515.415 379.778 m
516.415 378.778 l
517.415 379.778 l
516.415 380.778 l
515.415 379.778 l
S
516.415 379.778 m
516.415 379.778 l
S
517.415 379.878 m
518.415 378.878 l
519.415 379.878 l
518.415 380.878 l
517.415 379.878 l
S
518.415 379.878 m
518.415 379.878 l
S
519.515 379.878 m
520.515 378.878 l
521.515 379.878 l
520.515 380.878 l
519.515 379.878 l
S
520.515 379.878 m
520.515 379.878 l
S
521.515 380.378 m
522.515 379.378 l
523.515 380.378 l
522.515 381.378 l
521.515 380.378 l
S
522.515 380.378 m
522.515 380.378 l
S
560.015 381.978 m
561.015 380.978 l
562.015 381.978 l
561.015 382.978 l
560.015 381.978 l
S
561.015 381.978 m
561.015 381.978 l
S
593.415 382.778 m
594.415 381.778 l
595.415 382.778 l
594.415 383.778 l
593.415 382.778 l
S
594.415 382.778 m
594.415 382.778 l
S
626.915 383.278 m
627.915 382.278 l
628.915 383.278 l
627.915 384.278 l
626.915 383.278 l
S
627.915 383.278 m
627.915 383.278 l
S
660.315 383.578 m
661.315 382.578 l
662.315 383.578 l
661.315 384.578 l
660.315 383.578 l
S
661.315 383.578 m
661.315 383.578 l
S
U
u
1 1 1 1 K
512.315 383.978 m
512.315 383.978 l
512.315 82.978 l
S
U
1 Ap
0 O
0 0 0 1 k
0 J 0 j 1 w
142 82.6667 m
142.9763 82.6667 143.7678 83.4582 143.7678 84.4345 c
143.7678 85.4108 142.9763 86.2023 142 86.2023 c
141.0237 86.2023 140.2322 85.4108 140.2322 84.4345 c
140.2322 83.4582 141.0237 82.6667 142 82.6667 c
f
512.3333 81 m
513.3096 81 514.1011 81.7915 514.1011 82.7678 c
514.1011 83.7441 513.3096 84.5356 512.3333 84.5356 c
511.357 84.5356 510.5655 83.7441 510.5655 82.7678 c
510.5655 81.7915 511.357 81 512.3333 81 c
f
LB
%AI5_EndLayer--
%%PageTrailer
gsave annotatepage grestore showpage
%%Trailer
Adobe_Illustrator_AI5 /terminate get exec
Adobe_ColorImage_AI6 /terminate get exec
Adobe_typography_AI5 /terminate get exec
Adobe_cshow /terminate get exec
Adobe_level2_AI5 /terminate get exec
%%EOF

%%EndDocument
 @endspecial 2712 x Fx(Figure)642 b(2:)996 b(Mean)642
b(Euler)g(c)-36 b(haracteristic)643 b(p)36 b(er)642 b(site)g(and)g
(mean)g(b)36 b(ond)641 b(o)36 b(ccupation)4317 29486
y(n)-36 b(um)g(b)36 b(er)432 b(as)i(functions)f(of)i
Fu(\257)74 b Fx(,)433 b(for)i Fu(q)416 b Fx(=)369 b(5000)434
b(in)g(dimension)f Fu(d)369 b Fx(=)g(2.)6268 33287 y(F)-108
b(or)542 b(small)h(v)-72 b(alues)543 b(of)g Fu(q)590
b Fx(\(to)542 b(whic)-36 b(h)542 b(the)g(ab)36 b(o)-36
b(v)g(e)543 b(men)-36 b(tioned)542 b(analysis)h(do)36
b(es)543 b(not)4317 34892 y(apply\))466 b(it)g(w)-36
b(ould)465 b(b)36 b(e,)474 b(in)466 b(particular,)474
b(in)-36 b(teresting)465 b(to)h(see)g(if)g(the)g(mean)f(lo)36
b(cal)467 b(Euler-)4317 36497 y(P)-36 b(oincar)g(\266)-614
b(e)449 b(c)-36 b(haracteristic)448 b(is)g(con)-36 b(tin)g(uous)447
b(and)h(tak)-36 b(es)448 b(the)g(v)-72 b(alue)449 b(0)f(when)g(the)f
(transi-)4317 38102 y(tion)490 b(is)h(second)f(order,)504
b(as)491 b(it)f(is)h(the)e(case)i(for)g(the)f(p)36 b(ercolation)491
b(mo)36 b(del.)748 b(Numerical)4317 39707 y(sim)-36 b(ulations)500
b(p)36 b(erformed)499 b(in)g([BF)-36 b(G])500 b(indicate)f(that)g(this)
g(is)h(actually)g(the)f(case.)777 b(W)-108 b(e)4317 41312
y(illustrate)432 b(in)g(Figure)g(3)g(when)f Fu(d)369
b Fx(=)g(2)432 b(and)f Fu(q)417 b Fx(=)368 b(2)432 b(the)g(b)36
b(eha)-36 b(viour)432 b(of)g(the)f(mean)h(lo)36 b(cal)4317
42917 y(Euler-P)-36 b(oincar)g(\266)-614 b(e)419 b(c)-36
b(haracteristic)419 b(as)g(a)g(function)f(of)i(the)e(temp)36
b(erature)418 b(that)g(con\257rms)4317 44522 y(this)433
b(prediction.)6268 46725 y(In)541 b(the)g(n)-36 b(umerics)541
b(w)-36 b(e)541 b(ha)-36 b(v)g(e)542 b(directly)g(sampled)f(the)g(FK)g
(distribution)g(through)4317 48330 y(the)465 b(heat)f(bath)h(Mon)-36
b(te)464 b(Carlo)i(metho)36 b(d)464 b(\(Glaub)36 b(er)464
b(dynamics\).)673 b(As)465 b(w)-36 b(e)465 b(needed)f(the)4317
49935 y(n)-36 b(um)g(b)36 b(er)328 b(of)i(connected)e(comp)36
b(onen)-36 b(ts)329 b(to)g(compute)f(the)h(w)-36 b(eigh)g(ts)329
b(of)h(this)f(distribution,)4317 51540 y(the)433 b(Hoshen{Kop)36
b(elman)434 b([HK)q(])f(cluster)h(algorithm)g(has)g(b)36
b(een)433 b(used.)6268 53743 y(W)-108 b(e)429 b(think)g(that)f(the)h
(fact)g(that)g(the)f(mean)h(lo)36 b(cal)431 b(Euler-P)-36
b(oincar)g(\266)-614 b(e)428 b(c)-36 b(haracteristic)4317
55348 y(v)-72 b(anishes)391 b(at)g(the)f(transition)g(giv)-36
b(es)392 b(new)e(non)g(trivial)i(informations)f(on)g(the)f(top)36
b(ology)4317 56953 y(of)434 b(t)-36 b(ypical)435 b(con\257gurations)e
(at)h(this)f(p)36 b(oin)-36 b(t.)25253 70015 y(25)p eop
%%Page: 26 26
26 25 bop 16454 24181 a @beginspecial 115 @llx 214 @lly
469 @urx 555 @ury 1700 @rwi @setspecial
%%BeginDocument: chi2.eps
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: Adobe Illustrator(TM) 7.0
%%For: (--- - cpt) (cnrs)
%%Title: (chi2.eps)
%%CreationDate: (12/16/02) (2:39 PM)
%%BoundingBox: 115 214 469 555
%%HiResBoundingBox: 115.7061 214.0941 468.85 554.2239
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%DocumentFonts: Times-Italic
%%DocumentNeededFonts: Times-Italic
%%DocumentSuppliedResources: procset Adobe_level2_AI5 1.2 0
%%+ procset Adobe_typography_AI5 1.0 1
%%+ procset Adobe_ColorImage_AI6 1.1 0
%%+ procset Adobe_Illustrator_AI5 1.2 0
%%+ procset Adobe_cshow 2.0 8
%AI5_FileFormat 3.0
%AI3_ColorUsage: Color
%AI3_IncludePlacedImages
%AI7_ImageSettings: 1
%%CMYKCustomColor: 1 0 0.55 0 (Aigue-marine)
%%+ 1 0.5 0 0 (Bleu)
%%+ 0.8 0.05 0 0 (Bleu ciel)
%%+ 1 0.9 0.1 0 (Bleu fonc\216)
%%+ 0.5 0.4 0.3 0 (Bleu gris)
%%+ 0.5 0.85 1 0 (Marron)
%%+ 0.05 0.2 0.95 0 (Or)
%%+ 0 0.45 1 0 (Orange)
%%+ 0.15 1 1 0 (Rouge)
%%+ 1 0.55 1 0 (Vert)
%%+ 0.75 0.05 1 0 (Vert prairie)
%%+ 0.45 0.9 0 0 (Violet)
%%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set)
%%+ Options: 1 16 0 1 0 1 1 1 0 1 1 1 1 18 0 0 0 0 0 0 0 0 -1 -1
%%+ PPD: 1 21 0 0 60 45 2 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 ()
%AI3_TemplateBox: 300 225 300 225
%AI3_TileBox: 30 -165 568 616
%AI3_DocumentPreview: Macintosh_ColorPic
%AI5_ArtSize: 595 842
%AI5_RulerUnits: 2
%AI5_ArtFlags: 0 0 0 1 0 0 1 1 0
%AI5_TargetResolution: 800
%AI5_NumLayers: 1
%AI5_OpenToView: -228 633 -1 1146 725 18 1 1 3 40 0 0
%AI5_OpenViewLayers: 7
%%PageOrigin:30 -165
%%AI3_PaperRect:-28 811 567 -31
%%AI3_Margin:28 -30 -29 31
%AI7_GridSettings: 72 8 72 8 1 0 0.8 0.8 0.8 0.9 0.9 0.9
%%EndComments
%%BeginProlog
%%BeginResource: procset Adobe_level2_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation)
%%Version: 1.2 0
%%CreationDate: (04/10/93) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
userdict /Adobe_level2_AI5 25 dict dup begin
	put
	/packedarray where not
	{
		userdict begin
		/packedarray
		{
			array astore readonly
		} bind def
		/setpacking /pop load def
		/currentpacking false def
	 end
		0
	} if
	pop
	userdict /defaultpacking currentpacking put true setpacking
	/initialize
	{
		Adobe_level2_AI5 begin
	} bind def
	/terminate
	{
		currentdict Adobe_level2_AI5 eq
		{
		 end
		} if
	} bind def
	mark
	/setcustomcolor where not
	{
		/findcmykcustomcolor
		{
			0
			6 packedarray
		} bind def
		/findrgbcustomcolor
		{
			1
			5 packedarray
		} bind def
		/setcustomcolor
		{
			exch
			aload pop
			0 eq
			{
				pop
				4
				{
					4 index mul
					4 1 roll
				} repeat
				5 -1 roll pop
				setcmykcolor
			}
			{
				pop
				3
				{
					1 exch sub
					3 index mul
					1 exch sub
					3 1 roll
				} repeat
				4 -1 roll pop
				setrgbcolor
			} ifelse
		}
		def
	} if

	/gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def
	userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put
	userdict /level2?
	systemdict /languagelevel known dup
	{
		pop systemdict /languagelevel get 2 ge
	} if
	put
/level2ScreenFreq
{
 begin
		60
		HalftoneType 1 eq
		{
			pop Frequency
		} if
		HalftoneType 2 eq
		{
			pop GrayFrequency
		} if
		HalftoneType 5 eq
		{
			pop Default level2ScreenFreq
		} if
 end
} bind def
userdict /currentScreenFreq
	level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put
level2? not
	{
		/setcmykcolor where not
		{
			/setcmykcolor
			{
				exch .11 mul add exch .59 mul add exch .3 mul add
				1 exch sub setgray
			} def
		} if
		/currentcmykcolor where not
		{
			/currentcmykcolor
			{
				0 0 0 1 currentgray sub
			} def
		} if
		/setoverprint where not
		{
			/setoverprint /pop load def
		} if
		/selectfont where not
		{
			/selectfont
			{
				exch findfont exch
				dup type /arraytype eq
				{
					makefont
				}
				{
					scalefont
				} ifelse
				setfont
			} bind def
		} if
		/cshow where not
		{
			/cshow
			{
				[
				0 0 5 -1 roll aload pop
				] cvx bind forall
			} bind def
		} if
	} if
	cleartomark
	/anyColor?
	{
		add add add 0 ne
	} bind def
	/testColor
	{
		gsave
		setcmykcolor currentcmykcolor
		grestore
	} bind def
	/testCMYKColorThrough
	{
		testColor anyColor?
	} bind def
	userdict /composite?
	level2?
	{
		gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore
		add add add 4 eq
	}
	{
		1 0 0 0 testCMYKColorThrough
		0 1 0 0 testCMYKColorThrough
		0 0 1 0 testCMYKColorThrough
		0 0 0 1 testCMYKColorThrough
		and and and
	} ifelse
	put
	composite? not
	{
		userdict begin
		gsave
		/cyan? 1 0 0 0 testCMYKColorThrough def
		/magenta? 0 1 0 0 testCMYKColorThrough def
		/yellow? 0 0 1 0 testCMYKColorThrough def
		/black? 0 0 0 1 testCMYKColorThrough def
		grestore
		/isCMYKSep? cyan? magenta? yellow? black? or or or def
		/customColor? isCMYKSep? not def
	 end
	} if
 end defaultpacking setpacking
%%EndResource
%%BeginResource: procset Adobe_typography_AI5 1.0 1
%%Title: (Typography Operators)
%%Version: 1.0 1
%%CreationDate:(6/10/1996) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_typography_AI5 68 dict dup begin
put
/initialize
{
 begin
 begin
	Adobe_typography_AI5 begin
	Adobe_typography_AI5
	{
		dup xcheck
		{
			bind
		} if
		pop pop
	} forall
 end
 end
 end
	Adobe_typography_AI5 begin
} def
/terminate
{
	currentdict Adobe_typography_AI5 eq
	{
	 end
	} if
} def
/modifyEncoding
{
	/_tempEncode exch ddef
	/_pntr 0 ddef
	{
		counttomark -1 roll
		dup type dup /marktype eq
		{
			pop pop exit
		}
		{
			/nametype eq
			{
				_tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll
				put
			}
			{
				/_pntr exch ddef
			} ifelse
		} ifelse
	} loop
	_tempEncode
} def
/havefont
{
	systemdict /languagelevel known
		{
		/Font resourcestatus dup
			{ exch pop exch pop }
		if
		}
		{
		systemdict /FontDirectory get 1 index known
			{ pop true }
			{
			systemdict /fileposition known
				{
				dup length 6 add exch
				Ss 6 250 getinterval
				cvs pop
				Ss exch 0 exch getinterval
				status
					{ pop pop pop pop true }
					{ false }
				ifelse
				}
				{
				pop false
				}
			ifelse
			}
		ifelse
		}
	ifelse
} def
/TE
{
	StandardEncoding 256 array copy modifyEncoding
	/_nativeEncoding exch def
} def
/subststring {
	exch 2 index exch search
	{
		exch pop
		exch dup () eq
		{
			pop exch concatstring
		}
		{
			3 -1 roll
			exch concatstring
			concatstring
		} ifelse
		exch pop true
	}
	{
		pop pop false
	} ifelse
} def
/concatstring {
	1 index length 1 index length
	1 index add
	string
	dup 0 5 index putinterval
	dup 2 index 4 index putinterval
	4 1 roll pop pop pop
} def
%
/TZ
{
	dup type /arraytype eq
	{
		/_wv exch def
	}
	{
		/_wv 0 def
	} ifelse
	/_useNativeEncoding exch def
	2 index havefont
	{
		3 index
		255 string
		cvs

		dup
		(_Symbol_)
		eq
		{
			pop
			2 index
			findfont

		}
		{
			dup length 1 sub
			1 exch
			getinterval

			cvn
			findfont
		} ifelse
	}
	{
		dup 1 eq
		{
			2 index 64 string cvs
			dup (-90pv-RKSJ-) (-83pv-RKSJ-) subststring
			{
				exch pop dup havefont
				{
					findfont false
				}
				{
					pop true
				} ifelse
			}
			{
				pop	dup
				(-90ms-RKSJ-) (-Ext-RKSJ-) subststring
				{
					exch pop dup havefont
					{
						findfont false
					}
					{
						pop true
					} ifelse
				}
				{
					pop pop true
				} ifelse
			} ifelse
			{
				/Ryumin-Light-83pv-RKSJ-H havefont
					{/Ryumin-Light-83pv-RKSJ-H}
					{/Courier}
					ifelse
					findfont
					[1 0 0.5 1 0 0] makefont
			} if
		}
		{
			/Courier findfont
		} ifelse
	} ifelse
	_wv type /arraytype eq
	{
		_wv makeblendedfont
	} if
	dup length 10 add dict
 begin
	mark exch
	{
		1 index /FID ne
		{
			def
		} if
		cleartomark mark
	} forall
	pop
	/FontScript exch def
	/FontDirection exch def
	/FontRequest exch def
	/FontName exch def
	counttomark 0 eq
	{
		1 _useNativeEncoding eq
		{
			/Encoding _nativeEncoding def
		} if
		cleartomark
	}
	{
		/Encoding load 256 array copy
		modifyEncoding /Encoding exch def
	} ifelse
	FontName currentdict
 end
	definefont pop
} def
/tr
{
	_ax _ay 3 2 roll
} def
/trj
{
	_cx _cy _sp _ax _ay 6 5 roll
} def
/a0
{
	/Tx
	{
		dup
		currentpoint 3 2 roll
		tr _psf
		newpath moveto
		tr _ctm _pss
	} ddef
	/Tj
	{
		dup
		currentpoint 3 2 roll
		trj _pjsf
		newpath moveto
		trj _ctm _pjss
	} ddef
} def
/a1
{
W B
} def
/e0
{
	/Tx
	{
		tr _psf
	} ddef
	/Tj
	{
		trj _pjsf
	} ddef
} def
/e1
{
W F
} def
/i0
{
	/Tx
	{
		tr sp
	} ddef
	/Tj
	{
		trj jsp
	} ddef
} def
/i1
{
	W N
} def
/o0
{
	/Tx
	{
		tr sw rmoveto
	} ddef
	/Tj
	{
		trj swj rmoveto
	} ddef
} def
/r0
{
	/Tx
	{
		tr _ctm _pss
	} ddef
	/Tj
	{
		trj _ctm _pjss
	} ddef
} def
/r1
{
W S
} def
/To
{
	pop _ctm currentmatrix pop
} def
/TO
{
	iTe _ctm setmatrix newpath
} def
/Tp
{
	pop _tm astore pop _ctm setmatrix
	_tDict begin
	/W
	{
	} def
	/h
	{
	} def
} def
/TP
{
 end
	iTm 0 0 moveto
} def
/Tr
{
	_render 3 le
	{
		currentpoint newpath moveto
	} if
	dup 8 eq
	{
		pop 0
	}
	{
		dup 9 eq
		{
			pop 1
		} if
	} ifelse
	dup /_render exch ddef
	_renderStart exch get load exec
} def
/iTm
{
	_ctm setmatrix _tm concat
	_shift aload pop _lineorientation 1 eq { exch } if translate
	_scale aload pop _lineorientation 1 eq _yokoorientation 1 eq or { exch } if scale
} def
/Tm
{
	_tm astore pop iTm 0 0 moveto
} def
/Td
{
	_mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto
} def
/iTe
{
	_render -1 eq
	{
	}
	{
		_renderEnd _render get dup null ne
		{
			load exec
		}
		{
			pop
		} ifelse
	} ifelse
	/_render -1 ddef
} def
/Ta
{
	pop
} def
/Tf
{
	1 index type /nametype eq
	{
		dup 0.75 mul 1 index 0.25 mul neg
	} if
	/_fontDescent exch ddef
	/_fontAscent exch ddef
	/_fontSize exch ddef
	/_fontRotateAdjust _fontAscent _fontDescent add 2 div neg ddef
	/_fontHeight _fontSize ddef
	findfont _fontSize scalefont setfont
} def
/Tl
{
	pop neg 0 exch
	_leading astore pop
} def
/Tt
{
	pop
} def
/TW
{
	3 npop
} def
/Tw
{
	/_cx exch ddef
} def
/TC
{
	3 npop
} def
/Tc
{
	/_ax exch ddef
} def
/Ts
{
	0 exch
	_shift astore pop
	currentpoint
	iTm
	moveto
} def
/Ti
{
	3 npop
} def
/Tz
{
	count 1 eq { 100 } if
	100 div exch 100 div exch
	_scale astore pop
	iTm
} def
/TA
{
	pop
} def
/Tq
{
	pop
} def
/Tg
{
	pop
} def
/TG
{
	pop
} def
/Tv
{
	/_lineorientation exch ddef
} def
/TV
{
	/_charorientation exch ddef
} def
/Ty
{
	dup /_yokoorientation exch ddef 1 sub neg Tv
} def
/TY
{
	pop
} def
/T~
{
	Tx
} def
/Th
{
	pop pop pop pop pop
} def
/TX
{
	pop
} def
/Tk
{
	_fontSize mul 1000 div
	_lineorientation 0 eq { neg 0 } { 0 exch } ifelse
	rmoveto
	pop
} def
/TK
{
	2 npop
} def
/T*
{
	_leading aload pop
	_lineorientation 0 ne { exch } if
	Td
} def
/T*-
{
	_leading aload pop
	_lineorientation 0 ne { exch } if
	exch neg exch neg
	Td
} def
/T-
{
	_ax neg 0 rmoveto
	_lineorientation 1 eq _charorientation 0 eq and { 1 TV _hyphen Tx 0 TV } { _hyphen Tx } ifelse
} def
/T+
{
} def
/TR
{
	_ctm currentmatrix pop
	_tm astore pop
	iTm 0 0 moveto
} def
/TS
{
	currentfont 3 1 roll
	/_Symbol_ findfont _fontSize scalefont setfont

	0 eq
	{
		Tx
	}
	{
		Tj
	} ifelse
	setfont
} def
/Xb
{
	pop pop
} def
/Tb /Xb load def
/Xe
{
	pop pop pop pop
} def
/Te /Xe load def
/XB
{
} def
/TB /XB load def
currentdict readonly pop
end
setpacking
%
/X^
{
	currentfont 5 1 roll
	dup havefont
		{
		findfont _fontSize scalefont setfont
		}
		{
		pop
		exch
		} ifelse
	2 index 0 eq
	{
		Tx
	}
	{
		Tj
	} ifelse
	pop	pop
	setfont
} def
/T^	/X^	load def
%%EndResource
%%BeginProcSet: Adobe_ColorImage_AI6 1.1 0
userdict /Adobe_ColorImage_AI6 known not
{
	userdict /Adobe_ColorImage_AI6 24 dict put
} if
userdict /Adobe_ColorImage_AI6 get begin
/initialize
{
	Adobe_ColorImage_AI6 begin
	Adobe_ColorImage_AI6
	{
		dup type /arraytype eq
		{
			dup xcheck
			{
				bind
			} if
		} if
		pop pop
	} forall
} def
/terminate { end } def
currentdict /Adobe_ColorImage_AI6_Vars known not
{
	/Adobe_ColorImage_AI6_Vars 15 dict def
} if
Adobe_ColorImage_AI6_Vars begin
	/channelcount 0 def
	/sourcecount 0 def
	/sourcearray 4 array def
	/plateindex -1 def
	/XIMask 0 def
	/XIBinary 0 def
	/XIChannelCount 0 def
	/XIBitsPerPixel 0 def
	/XIImageHeight 0 def
	/XIImageWidth 0 def
	/XIImageMatrix null def
	/XIBuffer null def
	/XIDataProc null def
	/XIVersion 6 def
end
/WalkRGBString null def
/WalkCMYKString null def
/StuffRGBIntoGrayString null def
/RGBToGrayImageProc null def
/StuffCMYKIntoGrayString null def
/CMYKToGrayImageProc null def
/ColorImageCompositeEmulator null def
/SeparateCMYKImageProc null def
/FourEqual null def
/TestPlateIndex null def
currentdict /_colorimage known not
{
	/colorimage where
	{
		/colorimage get /_colorimage exch def
	}
	{
		/_colorimage null def
	} ifelse
} if
/_currenttransfer systemdict /currenttransfer get def
/colorimage null def
/XI null def
/WalkRGBString
{
	0 3 index
	dup length 1 sub 0 3 3 -1 roll
	{
		3 getinterval { } forall
		5 index exec
		3 index
	} for

	 5 { pop } repeat
} def
/WalkCMYKString
{
	0 3 index
	dup length 1 sub 0 4 3 -1 roll
	{
		4 getinterval { } forall

		6 index exec

		3 index

	} for

	5 { pop } repeat

} def
/StuffRGBIntoGrayString
{
	.11 mul exch

	.59 mul add exch

	.3 mul add

	cvi 3 copy put

	pop 1 add
} def
/RGBToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 3 idiv string
		dup 3 1 roll

		/StuffRGBIntoGrayString load exch
		WalkRGBString
 end
} def
/StuffCMYKIntoGrayString
{
	exch .11 mul add

	exch .59 mul add

	exch .3 mul add

	dup 255 gt { pop 255 } if

	255 exch sub cvi 3 copy put

	pop 1 add
} def
/CMYKToGrayImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcearray 0 get exec
		dup length 4 idiv string
		dup 3 1 roll

		/StuffCMYKIntoGrayString load exch
		WalkCMYKString
 end
} def
/ColorImageCompositeEmulator
{
	pop true eq
	{
		Adobe_ColorImage_AI6_Vars /sourcecount get 5 add { pop } repeat
	}
	{
		Adobe_ColorImage_AI6_Vars /channelcount get 1 ne
		{
			Adobe_ColorImage_AI6_Vars begin
				sourcearray 0 3 -1 roll put

				channelcount 3 eq
				{
					/RGBToGrayImageProc
				}
				{
					/CMYKToGrayImageProc
				} ifelse
				load
		 end
		} if
		image
	} ifelse
} def
/SeparateCMYKImageProc
{
	Adobe_ColorImage_AI6_Vars begin
		sourcecount 0 ne
		{
			sourcearray plateindex get exec
		}
		{
			sourcearray 0 get exec

			dup length 4 idiv string

			0 2 index

			plateindex 4 2 index length 1 sub
			{
				get 255 exch sub

				3 copy put pop 1 add

				2 index
			} for
			pop pop exch pop
		} ifelse
 end
} def

/FourEqual
{
	4 index ne
	{
		pop pop pop false
	}
	{
		4 index ne
		{
			pop pop false
		}
		{
			4 index ne
			{
				pop false
			}
			{
				4 index eq
			} ifelse
		} ifelse
	} ifelse
} def
/TestPlateIndex
{
	Adobe_ColorImage_AI6_Vars begin
		/plateindex -1 def
		/setcmykcolor where
		{
			pop
			gsave
			1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub
			0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub
			grestore
			1 0 0 0 FourEqual
			{
				/plateindex 0 def
			}
			{
				0 1 0 0 FourEqual
				{
					/plateindex 1 def
				}
				{
					0 0 1 0 FourEqual
					{
						/plateindex 2 def
					}
					{
						0 0 0 1 FourEqual
						{
							/plateindex 3 def
						}
						{
							0 0 0 0 FourEqual
							{
								/plateindex 5 def
							} if
						} ifelse
					} ifelse
				} ifelse
			} ifelse
			pop pop pop pop
		} if
		plateindex
 end
} def
/colorimage
{
	Adobe_ColorImage_AI6_Vars begin
		/channelcount 1 index def
		/sourcecount 2 index 1 eq { channelcount 1 sub } { 0 } ifelse def
		4 sourcecount add index dup
		8 eq exch 1 eq or not
 end

	{
		/_colorimage load null ne
		{
			_colorimage
		}
		{
			Adobe_ColorImage_AI6_Vars /sourcecount get
			7 add { pop } repeat
		} ifelse
	}
	{
		dup 3 eq
		TestPlateIndex
		dup -1 eq exch 5 eq or or
		{
			/_colorimage load null eq
			{
				ColorImageCompositeEmulator
			}
			{
				dup 1 eq
				{
					pop pop image
				}
				{
					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						gsave

						0 _currenttransfer exec
						1 _currenttransfer exec
						eq
						{ 0 _currenttransfer exec 0.5 lt }
						{ 0 _currenttransfer exec 1 _currenttransfer exec gt } ifelse

						{ { pop 0 } } { { pop 1 } } ifelse
						systemdict /settransfer get exec
					} if

					_colorimage

					Adobe_ColorImage_AI6_Vars /plateindex get 5 eq
					{
						grestore
					} if
				} ifelse
			} ifelse
		}
		{
			dup 1 eq
			{
				pop pop
				image
			}
			{
				pop pop
				Adobe_ColorImage_AI6_Vars begin
					sourcecount -1 0
					{
						exch sourcearray 3 1 roll put
					} for
					/SeparateCMYKImageProc load
			 end
				systemdict /image get exec
			} ifelse
		} ifelse
	} ifelse
} def
/XG
{
	pop pop
} def
/XF
{
	13 {pop} repeat
} def
/Xh
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIImageHeight exch def
		/XIImageWidth exch def
		/XIImageMatrix exch def
		0 0 moveto
		XIImageMatrix concat
		XIImageWidth XIImageHeight scale

		XIMask
		{
			/_lp /null ddef
			_fc
			/_lp /imagemask ddef
		}
		if
		/XIVersion 7 def
 end
} def
/XH
{
	Adobe_ColorImage_AI6_Vars begin
		/XIVersion 6 def
		grestore
 end
} def
/XI
{
	Adobe_ColorImage_AI6_Vars begin
		gsave
		/XIMask exch 0 ne def
		/XIBinary exch 0 ne def
		pop
		pop
		/XIChannelCount exch def
		/XIBitsPerPixel exch def
		/XIImageHeight exch def
		/XIImageWidth exch def
		pop pop pop pop
		/XIImageMatrix exch def
		XIBitsPerPixel 1 eq
		{
			XIImageWidth 8 div ceiling cvi
		}
		{
			XIImageWidth XIChannelCount mul
		} ifelse
		/XIBuffer exch string def
		XIBinary
		{
			/XIDataProc { currentfile XIBuffer readstring pop } def
			XIVersion 6 le
			{
				currentfile 128 string readline pop pop
			}
			if
		}
		{
			/XIDataProc { currentfile XIBuffer readhexstring pop } def
		} ifelse

		XIVersion 6 le
		{
			0 0 moveto
			XIImageMatrix concat
			XIImageWidth XIImageHeight scale
			XIMask
			{
				/_lp /null ddef
				_fc
				/_lp /imagemask ddef
			} if
		} if

		XIMask
		{
			XIImageWidth XIImageHeight
			false
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load
			imagemask
		}
		{
			XIImageWidth XIImageHeight
			XIBitsPerPixel
			[ XIImageWidth 0 0 XIImageHeight neg 0 0 ]
			/XIDataProc load

			XIChannelCount 1 eq
			{
				gsave
				0 setgray
				image
				grestore
			}
			{
				false
				XIChannelCount
				colorimage
			} ifelse
		} ifelse
		grestore
 end
} def
end
%%EndProcSet
%%BeginResource: procset Adobe_Illustrator_AI5 1.2 0
%%Title: (Adobe Illustrator (R) Version 7.0 Full Prolog)
%%Version: 1.2 0
%%CreationDate: (3/7/1994) ()
%%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_Illustrator_AI5_vars 107 dict dup begin
put
/_eo false def
/_lp /none def
/_pf
{
} def
/_ps
{
} def
/_psf
{
} def
/_pss
{
} def
/_pjsf
{
} def
/_pjss
{
} def
/_pola 0 def
/_doClip 0 def
/cf currentflat def
/_lineorientation 0 def
/_charorientation 0 def
/_yokoorientation 0 def
/_tm matrix def
/_renderStart
[
/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0
] def
/_renderEnd
[
null null null null /i1 /i1 /i1 /i1
] def
/_render -1 def
/_shift [0 0] def
/_ax 0 def
/_ay 0 def
/_cx 0 def
/_cy 0 def
/_leading
[
0 0
] def
/_ctm matrix def
/_mtx matrix def
/_sp 16#020 def
/_hyphen (-) def
/_fontSize 0 def
/_fontAscent 0 def
/_fontDescent 0 def
/_fontHeight 0 def
/_fontRotateAdjust 0 def
/Ss 256 string def
Ss 0 (fonts/) putinterval
/_cnt 0 def
/_scale [1 1] def
/_nativeEncoding 0 def
/_useNativeEncoding 0 def
/_tempEncode 0 def
/_pntr 0 def
/_tDict 2 dict def
/_hfname 100 string def
/_hffound false def
/Tx
{
} def
/Tj
{
} def
/CRender
{
} def
/_AI3_savepage
{
} def
/_gf null def
/_cf 4 array def
/_rgbf 3 array def
/_if null def
/_of false def
/_fc
{
} def
/_gs null def
/_cs 4 array def
/_rgbs 3 array def
/_is null def
/_os false def
/_sc
{
} def
/_pd 1 dict def
/_ed 15 dict def
/_pm matrix def
/_fm null def
/_fd null def
/_fdd null def
/_sm null def
/_sd null def
/_sdd null def
/_i null def
/_lobyte 0 def
/_hibyte 0 def
/_cproc null def
/_cscript 0 def
/_hvax 0 def
/_hvay 0 def
/_hvwb 0 def
/_hvcx 0 def
/_hvcy 0 def
/_bitfont null def
/_bitlobyte 0 def
/_bithibyte 0 def
/_bitkey null def
/_bitdata null def
/_bitindex 0 def
/discardSave null def
/buffer 256 string def
/beginString null def
/endString null def
/endStringLength null def
/layerCnt 1 def
/layerCount 1 def
/perCent (%) 0 get def
/perCentSeen? false def
/newBuff null def
/newBuffButFirst null def
/newBuffLast null def
/clipForward? false def
end
userdict /Adobe_Illustrator_AI5 known not {
	userdict /Adobe_Illustrator_AI5 95 dict put
} if
userdict /Adobe_Illustrator_AI5 get begin
/initialize
{
	Adobe_Illustrator_AI5 dup begin
	Adobe_Illustrator_AI5_vars begin
	discardDict
	{
		bind pop pop
	} forall
	dup /nc get begin
	{
		dup xcheck 1 index type /operatortype ne and
		{
			bind
		} if
		pop pop
	} forall
 end
	newpath
} def
/terminate
{
 end
 end
} def
/_
null def
/ddef
{
	Adobe_Illustrator_AI5_vars 3 1 roll put
} def
/xput
{
	dup load dup length exch maxlength eq
	{
		dup dup load dup
		length 2 mul dict copy def
	} if
	load begin
	def
 end
} def
/npop
{
	{
		pop
	} repeat
} def
/hswj
{
	dup stringwidth 3 2 roll
	{
		_hvwb eq { exch _hvcx add exch _hvcy add } if
		exch _hvax add exch _hvay add
	} cforall
} def
/vswj
{
	0 0 3 -1 roll
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			dup cstring stringwidth 5 2 roll
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			4 -1 roll sub exch
			3 -1 roll sub exch
		}
		{
			_hvwb eq { exch _hvcy sub exch _hvcx sub } if
			exch _hvay sub exch _hvax sub
			_fontHeight sub
		} ifelse
	} cforall
} def
/swj
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hswj } { vswj } ifelse
} def
/sw
{
	0 0 0 6 3 roll swj
} def
/vjss
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			gsave
			false charpath currentpoint
			5 index setmatrix stroke
			grestore
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			gsave
			2 index false charpath
			6 index setmatrix stroke
			grestore

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjss
{
	4 1 roll
	{
		dup cstring
		gsave
		false charpath currentpoint
		5 index setmatrix stroke
		grestore
		moveto
		_sp eq
		{
			5 index 5 index rmoveto
		} if
		2 copy rmoveto
	} cforall
	6 npop
} def
/jss
{
	_lineorientation 0 eq { hjss } { vjss } ifelse
} def
/ss
{
	0 0 0 7 3 roll jss
} def
/vjsp
{
	4 1 roll
	{
		dup cstring
		dup length 1 eq
		_charorientation 1 eq
		and
		{
			-90 rotate
			currentpoint
			_fontRotateAdjust add
			moveto
			false charpath
            currentpoint
			_fontRotateAdjust sub
			moveto
			_sp eq
			{
				5 index 5 index rmoveto
			} if
			2 copy rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			5 index sub
			3 index _sp eq
			{
				9 index sub
			} if

			currentpoint
			exch 4 index stringwidth pop 2 div sub
			exch _fontAscent sub
			moveto

			2 index false charpath

			moveto pop pop
		} ifelse
	} cforall
	6 npop
} def
/hjsp
{
    4 1 roll
    {
        dup cstring
        false charpath
        _sp eq
        {
            5 index 5 index rmoveto
        } if
        2 copy rmoveto
    } cforall
    6 npop
} def
/jsp
{
	matrix currentmatrix
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/sp
{
    matrix currentmatrix
    0 0 0 7 3 roll
    _lineorientation 0 eq {hjsp} {vjsp} ifelse
} def
/pl
{
	transform
	0.25 sub round 0.25 add exch
	0.25 sub round 0.25 add exch
	itransform
} def
/setstrokeadjust where
{
	pop true setstrokeadjust
	/c
	{
		curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll curveto
	} def
	/V
	/v load def
	/y
	{
		2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		lineto
	} def
	/L
	/l load def
	/m
	{
		moveto
	} def
}
{
	/c
	{
		pl curveto
	} def
	/C
	/c load def
	/v
	{
		currentpoint 6 2 roll pl curveto
	} def
	/V
	/v load def
	/y
	{
		pl 2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
		pl lineto
	} def
	/L
	/l load def
	/m
	{
		pl moveto
	} def
} ifelse
/d
{
	setdash
} def
/cf
{
} def
/i
{
	dup 0 eq
	{
		pop cf
	} if
	setflat
} def
/j
{
	setlinejoin
} def
/J
{
	setlinecap
} def
/M
{
	setmiterlimit
} def
/w
{
	setlinewidth
} def
/XR
{
	0 ne
	/_eo exch ddef
} def
/H
{
} def
/h
{
	closepath
} def
/N
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			_eo {eoclip} {clip} ifelse /_doClip 0 ddef
		} if
		newpath
	}
	{
		/CRender
		{
			N
		} ddef
	} ifelse
} def
/n
{
	N
} def
/F
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc
			/_doClip 0 ddef
		}
		{
			_pf
		} ifelse
	}
	{
		/CRender
		{
			F
		} ddef
	} ifelse
} def
/f
{
	closepath
	F
} def
/S
{
	_pola 0 eq
	{
		_doClip 1 eq
		{
			gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			_ps
		} ifelse
	}
	{
		/CRender
		{
			S
		} ddef
	} ifelse
} def
/s
{
	closepath
	S
} def
/B
{
	_pola 0 eq
	{
		_doClip 1 eq
		gsave F grestore
		{
			gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc
			/_doClip 0 ddef
		}
		{
			S
		} ifelse
	}
	{
		/CRender
		{
			B
		} ddef
	} ifelse
} def
/b
{
	closepath
	B
} def
/W
{
	/_doClip 1 ddef
} def
/*
{
	count 0 ne
	{
		dup type /stringtype eq
		{
			pop
		} if
	} if
	newpath
} def
/u
{
} def
/U
{
} def
/q
{
	_pola 0 eq
	{
		gsave
	} if
} def
/Q
{
	_pola 0 eq
	{
		grestore
	} if
} def
/*u
{
	_pola 1 add /_pola exch ddef
} def
/*U
{
	_pola 1 sub /_pola exch ddef
	_pola 0 eq
	{
		CRender
	} if
} def
/D
{
	pop
} def
/*w
{
} def
/*W
{
} def
/`
{
	/_i save ddef
	clipForward?
	{
		nulldevice
	} if
	6 1 roll 4 npop
	concat pop
	userdict begin
	/showpage
	{
	} def
	0 setgray
	0 setlinecap
	1 setlinewidth
	0 setlinejoin
	10 setmiterlimit
	[] 0 setdash
	/setstrokeadjust where {pop false setstrokeadjust} if
	newpath
	0 setgray
	false setoverprint
} def
/~
{
 end
	_i restore
} def
/O
{
	0 ne
	/_of exch ddef
	/_lp /none ddef
} def
/R
{
	0 ne
	/_os exch ddef
	/_lp /none ddef
} def
/g
{
	/_gf exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_gf setgray
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/G
{
	/_gs exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_gs setgray
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/k
{
	_cf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_cf aload pop setcmykcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/K
{
	_cs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_cs aload pop setcmykcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/Xa
{
	_rgbf astore pop
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_rgbf aload pop setrgbcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XA
{
	_rgbs astore pop
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_rgbs aload pop setrgbcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/_rgbtocmyk
{
3
	{
	1 exch sub 3 1 roll
	} repeat
3 copy 1 4 1 roll
3
	{
	3 index 2 copy gt
		{
		exch
		} if
	pop 4 1 roll
	} repeat
pop pop pop
4 1 roll
3
	{
	3 index sub
	3 1 roll
	} repeat
4 -1 roll
} def
/Xx
{
	exch
	/_gf exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/XX
{
	exch
	/_gs exch ddef
	0 eq
	{
		findcmykcustomcolor
	}
	{
		/findrgbcustomcolor where not {
			4 1 roll _rgbtocmyk
			5 -1 roll
			findcmykcustomcolor
		}
		{
			pop
			findrgbcustomcolor
		} ifelse
	} ifelse
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/x
{
	/_gf exch ddef
	findcmykcustomcolor
	/_if exch ddef
	/_fc
	{
		_lp /fill ne
		{
			_of setoverprint
			_if _gf 1 exch sub setcustomcolor
			/_lp /fill ddef
		} if
	} ddef
	/_pf
	{
		_fc
		_eo {eofill} {fill} ifelse
	} ddef
	/_psf
	{
		_fc
		hvashow
	} ddef
	/_pjsf
	{
		_fc
		hvawidthshow
	} ddef
	/_lp /none ddef
} def
/X
{
	/_gs exch ddef
	findcmykcustomcolor
	/_is exch ddef
	/_sc
	{
		_lp /stroke ne
		{
			_os setoverprint
			_is _gs 1 exch sub setcustomcolor
			/_lp /stroke ddef
		} if
	} ddef
	/_ps
	{
		_sc
		stroke
	} ddef
	/_pss
	{
		_sc
		ss
	} ddef
	/_pjss
	{
		_sc
		jss
	} ddef
	/_lp /none ddef
} def
/A
{
	pop
} def
/annotatepage
{
userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse
} def
/XT {
	pop pop
} def
/discard
{
	save /discardSave exch store
	discardDict begin
	/endString exch store
	gt38?
	{
		2 add
	} if
	load
	stopped
	pop
 end
	discardSave restore
} bind def
userdict /discardDict 7 dict dup begin
put
/pre38Initialize
{
	/endStringLength endString length store
	/newBuff buffer 0 endStringLength getinterval store
	/newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store
	/newBuffLast newBuff endStringLength 1 sub 1 getinterval store
} def
/shiftBuffer
{
	newBuff 0 newBuffButFirst putinterval
	newBuffLast 0
	currentfile read not
	{
	stop
	} if
	put
} def
0
{
	pre38Initialize
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff endString eq
			{
				cleartomark stop
			} if
			shiftBuffer
		} loop
	}
	{
	stop
	} ifelse
} def
1
{
	pre38Initialize
	/beginString exch store
	mark
	currentfile newBuff readstring exch pop
	{
		{
			newBuff beginString eq
			{
				/layerCount dup load 1 add store
			}
			{
				newBuff endString eq
				{
					/layerCount dup load 1 sub store
					layerCount 0 eq
					{
						cleartomark stop
					} if
				} if
			} ifelse
			shiftBuffer
		} loop
	} if
} def
2
{
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		endString eq
		{
			cleartomark stop
		} if
	} loop
} def
3
{
	/beginString exch store
	/layerCnt 1 store
	mark
	{
		currentfile buffer readline not
		{
		stop
		} if
		dup beginString eq
		{
			pop /layerCnt dup load 1 add store
		}
		{
			endString eq
			{
				layerCnt 1 eq
				{
					cleartomark stop
				}
				{
					/layerCnt dup load 1 sub store
				} ifelse
			} if
		} ifelse
	} loop
} def
end
userdict /clipRenderOff 15 dict dup begin
put
{
	/n /N /s /S /f /F /b /B
}
{
	{
		_doClip 1 eq
		{
			/_doClip 0 ddef _eo {eoclip} {clip} ifelse
		} if
		newpath
	} def
} forall
/Tr /pop load def
/Bb {} def
/BB /pop load def
/Bg {12 npop} def
/Bm {6 npop} def
/Bc /Bm load def
/Bh {4 npop} def
end
/Lb
{
	4 npop
	6 1 roll
	pop
	4 1 roll
	pop pop pop
	0 eq
	{
		0 eq
		{
			(%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard
		}
		{

			/clipForward? true def

			/Tx /pop load def
			/Tj /pop load def

			currentdict end clipRenderOff begin begin
		} ifelse
	}
	{
		0 eq
		{
			save /discardSave exch store
		} if
	} ifelse
} bind def
/LB
{
	discardSave dup null ne
	{
		restore
	}
	{
		pop
		clipForward?
		{
			currentdict
		 end
		 end
		 begin

			/clipForward? false ddef
		} if
	} ifelse
} bind def
/Pb
{
	pop pop
	0 (%AI5_EndPalette) discard
} bind def
/Np
{
	0 (%AI5_End_NonPrinting--) discard
} bind def
/Ln /pop load def
/Ap
/pop load def
/Ar
{
	72 exch div
	0 dtransform dup mul exch dup mul add sqrt
	dup 1 lt
	{
		pop 1
	} if
	setflat
} def
/Mb
{
	q
} def
/Md
{
} def
/MB
{
	Q
} def
/nc 4 dict def
nc begin
/setgray
{
	pop
} bind def
/setcmykcolor
{
	4 npop
} bind def
/setrgbcolor
{
	3 npop
} bind def
/setcustomcolor
{
	2 npop
} bind def
currentdict readonly pop
end
end
setpacking
%%EndResource
%%BeginResource: procset Adobe_cshow 2.0 8
%%Title: (Writing System Operators)
%%Version: 2.0 8
%%CreationDate: (1/23/89) ()
%%Copyright: ((C) 1992-1996 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_cshow 14 dict dup begin put
/initialize
{
	Adobe_cshow begin
	Adobe_cshow
	{
		dup xcheck
		{
			bind
		} if
		pop pop
	} forall
 end
	Adobe_cshow begin
} def
/terminate
{
currentdict Adobe_cshow eq
	{
 end
	} if
} def
/cforall
{
	/_lobyte 0 ddef
	/_hibyte 0 ddef
	/_cproc exch ddef
	/_cscript currentfont /FontScript known { currentfont /FontScript get } { -1 } ifelse ddef
	{
		/_lobyte exch ddef
		_hibyte 0 eq
		_cscript 1 eq
		_lobyte 129 ge _lobyte 159 le and
		_lobyte 224 ge _lobyte 252 le and or and
		_cscript 2 eq
		_lobyte 161 ge _lobyte 254 le and and
		_cscript 3 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript 25 eq
		_lobyte 161 ge _lobyte 254 le and and
    	_cscript -1 eq
		or or or or and
		{
			/_hibyte _lobyte ddef
		}
		{
			_hibyte 256 mul _lobyte add
			_cproc
			/_hibyte 0 ddef
		} ifelse
	} forall
} def
/cstring
{
	dup 256 lt
	{
		(s) dup 0 4 3 roll put
	}
	{
		dup 256 idiv exch 256 mod
		(hl) dup dup 0 6 5 roll put 1 4 3 roll put
	} ifelse
} def
/clength
{
	0 exch
	{ 256 lt { 1 } { 2 } ifelse add } cforall
} def
/hawidthshow
{
	{
		dup cstring
		show
		_hvax _hvay rmoveto
		_hvwb eq { _hvcx _hvcy rmoveto } if
	} cforall
} def
/vawidthshow
{
	{
		dup 255 le
		_charorientation 1 eq
		and
		{
			-90 rotate
			0 _fontRotateAdjust rmoveto
			cstring
			_hvcx _hvcy _hvwb _hvax _hvay 6 -1 roll awidthshow
			0 _fontRotateAdjust neg rmoveto
			90 rotate
		}
		{
			currentpoint
			_fontHeight sub
			exch _hvay sub exch _hvax sub
			2 index _hvwb eq { exch _hvcy sub exch _hvcx sub } if
			3 2 roll
			cstring
			dup stringwidth pop 2 div neg _fontAscent neg rmoveto
			show
			moveto
		} ifelse
	} cforall
} def
/hvawidthshow
{
	6 1 roll
	/_hvay exch ddef
	/_hvax exch ddef
	/_hvwb exch ddef
	/_hvcy exch ddef
	/_hvcx exch ddef
	_lineorientation 0 eq { hawidthshow } { vawidthshow } ifelse
} def
/hvwidthshow
{
	0 0 3 -1 roll hvawidthshow
} def
/hvashow
{
	0 0 0 6 -3 roll hvawidthshow
} def
/hvshow
{
	0 0 0 0 0 6 -1 roll hvawidthshow
} def
currentdict readonly pop end
setpacking
%%EndResource
%%EndProlog
%%BeginSetup
%%IncludeFont: Times-Italic
Adobe_level2_AI5 /initialize get exec
Adobe_cshow /initialize get exec
Adobe_Illustrator_AI5_vars Adobe_Illustrator_AI5 Adobe_typography_AI5 /initialize get exec
Adobe_ColorImage_AI6 /initialize get exec
Adobe_Illustrator_AI5 /initialize get exec
[
39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis
/Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute
/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde
/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex
/udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef
/guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide
/.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright
/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand
/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex
/Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex
/Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla
/hungarumlaut/ogonek/caron
TE
%AI55J_Tsume: None
%AI3_BeginEncoding: _Times-Italic Times-Italic
[/_Times-Italic/Times-Italic 0 0 1 TZ
%AI3_EndEncoding AdobeType
[161/degree 173/notequal 176/infinity/plusminus/lessequal/greaterequal
181/mu/partialdiff/summation/product/pi/integral 189/Omega
195/radical 197/approxequal 198/Delta 214/divide/lozenge 240/apple
/_Symbol_/Symbol 0 0 0 TZ
%AI5_Begin_NonPrinting
Np
%AI3_BeginPattern: (Acailles)
(Acailles) 1.6 9.3475 48.088 55.8355 [
%AI3_Tile
(0 O 0 R  1 g
 1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 9.3475 m
1.6 55.8355 L
48.088 55.8355 L
48.088 9.3475 L
1.6 9.3475 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R  0 g
 0 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
17.0956 9.3475 m
12.8162 9.3475 9.3475 5.8787 9.3475 1.6 C
9.3475 5.8787 5.8787 9.3475 1.6 9.3475 C
1.6 13.6262 5.0687 17.095 9.3475 17.095 c
13.6268 17.095 17.0956 13.6262 17.0956 9.3475 C
s
32.5918 9.3475 m
28.3125 9.3475 24.8437 5.8787 24.8437 1.6 C
24.8437 5.8787 21.3743 9.3475 17.0956 9.3475 C
17.0956 13.6262 20.5644 17.095 24.8437 17.095 c
29.1224 17.095 32.5918 13.6262 32.5918 9.3475 C
s
48.088 9.3475 m
43.8087 9.3475 40.3399 5.8787 40.3399 1.6 C
40.3399 5.8787 36.8705 9.3475 32.5918 9.3475 C
32.5918 13.6262 36.0606 17.095 40.3399 17.095 c
44.6186 17.095 48.088 13.6262 48.088 9.3475 C
s
17.0956 40.3393 m
12.8162 40.3393 9.3475 36.8699 9.3475 32.5912 C
9.3475 36.8699 5.8787 40.3393 1.6 40.3393 C
1.6 44.6181 5.0687 48.0874 9.3475 48.0874 c
13.6268 48.0874 17.0956 44.6181 17.0956 40.3393 C
s
17.0956 24.8431 m
12.8162 24.8431 9.3475 21.3743 9.3475 17.095 C
9.3475 21.3743 5.8787 24.8431 1.6 24.8431 C
1.6 29.1218 5.0687 32.5912 9.3475 32.5912 c
13.6268 32.5912 17.0956 29.1218 17.0956 24.8431 C
s
32.5918 24.8431 m
28.3125 24.8431 24.8437 21.3743 24.8437 17.095 C
24.8437 21.3743 21.3743 24.8431 17.0956 24.8431 C
17.0956 29.1218 20.5644 32.5912 24.8437 32.5912 c
29.1224 32.5912 32.5918 29.1218 32.5918 24.8431 C
s
48.088 24.8431 m
43.8087 24.8431 40.3399 21.3743 40.3399 17.095 C
40.3399 21.3743 36.8705 24.8431 32.5918 24.8431 C
32.5918 29.1218 36.0606 32.5912 40.3399 32.5912 c
44.6186 32.5912 48.088 29.1218 48.088 24.8431 C
s
32.5918 40.3393 m
28.3125 40.3393 24.8437 36.8699 24.8437 32.5912 C
24.8437 36.8699 21.3743 40.3393 17.0956 40.3393 C
17.0956 44.6181 20.5644 48.0874 24.8437 48.0874 c
29.1224 48.0874 32.5918 44.6181 32.5918 40.3393 C
s
48.088 40.3393 m
43.8087 40.3393 40.3399 36.8699 40.3399 32.5912 C
40.3399 36.8699 36.8705 40.3393 32.5918 40.3393 C
32.5918 44.6181 36.0606 48.0874 40.3399 48.0874 c
44.6186 48.0874 48.088 44.6181 48.088 40.3393 C
s
17.0956 55.8355 m
12.8162 55.8355 9.3475 52.3662 9.3475 48.0874 C
9.3475 52.3662 5.8787 55.8355 1.6 55.8355 C
1.6 60.1143 5.0687 63.5836 9.3475 63.5836 c
13.6268 63.5836 17.0956 60.1143 17.0956 55.8355 C
s
32.5918 55.8355 m
28.3125 55.8355 24.8437 52.3662 24.8437 48.0874 C
24.8437 52.3662 21.3743 55.8355 17.0956 55.8355 C
17.0956 60.1143 20.5644 63.5836 24.8437 63.5836 c
29.1224 63.5836 32.5918 60.1143 32.5918 55.8355 C
s
48.088 55.8355 m
43.8087 55.8355 40.3399 52.3662 40.3399 48.0874 C
40.3399 52.3662 36.8705 55.8355 32.5918 55.8355 C
32.5918 60.1143 36.0606 63.5836 40.3399 63.5836 c
44.6186 63.5836 48.088 60.1143 48.088 55.8355 C
s
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Bandes transparentes)
(Bandes transparentes) 8.45 4.6001 80.45 76.6001 [
%AI3_Tile
(0 O 0 R  1 0.07 1 0 k
 1 0.07 1 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 3.6 w 4 M []0 d
%AI3_Note:
0 D
0 XR
8.2 8.2 m
80.7 8.2 L
S
8.2 22.6001 m
80.7 22.6001 L
S
8.2 37.0002 m
80.7 37.0002 L
S
8.2 51.4 m
80.7 51.4 L
S
8.2 65.8001 m
80.7 65.8001 L
S
8.2 15.4 m
80.7 15.4 L
S
8.2 29.8001 m
80.7 29.8001 L
S
8.2 44.2 m
80.7 44.2 L
S
8.2 58.6001 m
80.7 58.6001 L
S
8.2 73.0002 m
80.7 73.0002 L
S
%AI6_EndPatternLayer
) &
] E
%AI3_EndPattern
%AI3_BeginPattern: (Briques)
(Briques) 1.6 1.6 73.6 73.6 [
%AI3_Tile
(0 O 0 R  0.3 0.85 0.85 0 k
 0.3 0.85 0.85 0 K
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 1 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 1.6 m
1.6 73.6 L
73.6 73.6 L
73.6 1.6 L
1.6 1.6 L
f
%AI6_EndPatternLayer
) &
(0 O 0 R  1 g
 1 G
) @
(
%AI6_BeginPatternLayer
800 Ar
0 J 0 j 0.3 w 4 M []0 d
%AI3_Note:
0 D
0 XR
1.6 70.01 m
73.6 70.01 l
S
1.6 62.809 m
73.6 62.809 L
S
1.6 55.609 m
73.6 55.609 L
S
1.6 48.408 m
73.6 48.408 L
S
1.6 41.208 m
73.6 41.208 L
S
1.6 34.007 m
73.6 34.007 L
S
1.6 26.807 m
73.6 26.807 L
S
1.6 19.606 m
73.6 19.606 L
S
1.6 12.406 m
73.6 12.406 L
S
1.6 5.206 m
73.6 5.206 L
S
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1 1 1 1 K
168.8 536.3 m
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U
1 1 0 0 K
0.5 w
168.8 536.3 m
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187.8 531.6 m
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206.7 522.2 m
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225.7 507.3 m
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244.6 488.7 m
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339.4 321.7 m
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358.3 302.6 m
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1 1 1 1 K
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1 Ap
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0 R
1 1 1 1 K
1 J 1 j 0.5 w
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s
187.5 529.909 m
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s
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s
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s
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s
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s
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s
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s
320.25 351.3465 m
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s
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s
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s
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s
434.159 257.9715 m
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LB
%AI5_EndLayer--
%%PageTrailer
gsave annotatepage grestore showpage
%%Trailer
Adobe_Illustrator_AI5 /terminate get exec
Adobe_ColorImage_AI6 /terminate get exec
Adobe_typography_AI5 /terminate get exec
Adobe_cshow /terminate get exec
Adobe_level2_AI5 /terminate get exec
%%EOF

%%EndDocument
 @endspecial 4317 26893 a Fx(Figure)516 b(3:)744 b(Mean)515
b(Euler)h(c)-36 b(haracteristic)516 b(p)36 b(er)516 b(site)g(as)g
(function)g(of)h Fu(\257)74 b Fx(,)536 b(for)517 b Fu(q)557
b Fx(=)508 b(2)517 b(in)4317 28499 y(dimension)433 b
Fu(d)369 b Fx(=)g(2.)4317 33480 y Fk(Ac)-50 b(kno)g(wledgmen)g(ts)4317
36541 y Fx(The)376 b(authors)g(thank)g(Salv)-72 b(ador)376
b(Miracle{Sol)-36 b(\266)-614 b(e)377 b(for)g(helpful)f(discussions.)
559 b(W)-108 b(arm)376 b(hos-)4317 38146 y(pitalit)-36
b(y)368 b(and)e(Financial)h(supp)36 b(ort)365 b(from)i(the)g(BiBoS)f
(researc)-36 b(h)367 b(Cen)-36 b(ter,)380 b(Univ)-36
b(ersit)g(y)367 b(of)4317 39751 y(Bielefeld)451 b(and)e(Cen)-36
b(tre)449 b(de)g(Ph)-36 b(ysique)449 b(Th)-36 b(\266)-614
b(eorique,)455 b(CNRS)449 b(Marseille)i(are)e(gratefully)4317
41356 y(ac)-36 b(kno)g(wledged.)4317 46391 y Fy(References)4317
49865 y Fx([A)g(CCN])1735 b(M.)560 b(Aizenman,)592 b(J.T.)562
b(Cha)-36 b(y)g(es,)593 b(L.)560 b(Cha)-36 b(y)g(es,)592
b(C.M.)561 b(Newman,)593 b FA(Disc)-66 b(on-)10566 51470
y(tinuity)506 b(of)h(the)g(magnetization)e(in)i(one{dimensional)f
Fx(1)p Fu(=)p Fr(j)p Fu(x)327 b Fr(\241)g Fu(y)48 b Fr(j)43697
50988 y Fs(2)44730 51470 y FA(Ising)10566 53075 y(and)465
b(Potts)g(mo)-66 b(dels)p Fx(,)434 b(J.)g(Stat.)f(Ph)-36
b(ys.)434 b Fh(50)p Fx(,)g(1{40)h(\(1988\).)4317 55787
y([A])4552 b(P)-108 b(.S.)396 b(Aleksandro)-36 b(v,)404
b FA(Combinatorial)429 b(T)-100 b(op)-66 b(olo)g(gy)p
Fx(,)404 b(v)-36 b(ol)396 b(3,)404 b(Gra)-36 b(ylo)36
b(c)-36 b(k)397 b(Press,)10566 57392 y(Alban)-36 b(y)-108
b(,)434 b(1960.)4317 60104 y([B])4606 b(R.J.)429 b(Baxter,)g
FA(Exactly)459 b(solve)-66 b(d)460 b(mo)-66 b(dels)459
b(in)f(statistic)-66 b(al)458 b(me)-66 b(chanics)p Fx(,)428
b(New-)10566 61709 y(Y)-108 b(ork,)434 b(Academic)g(Press,)g(1982.)4317
64421 y([Be])4028 b(C.)434 b(Berge,)h FA(Gr)-66 b(aphes)p
Fx(,)434 b(P)-36 b(aris:)579 b(Gauthier-Villars,)433
b(1983.)25253 70015 y(26)p eop
%%Page: 27 27
27 26 bop 4317 7306 a Fx([BF)-36 b(G])2772 b(Ph.)580
b(Blanc)-36 b(hard,)617 b(S.)580 b(F)-108 b(ortunato,)616
b(and)579 b(D.)i(Gandolfo,)617 b FA(Euler-Poinc)-66 b(ar)-33
b(\266)-631 b(e)10566 8911 y(char)-66 b(acteristic)349
b(and)h(phase)i(tr)-66 b(ansition)349 b(in)g(the)i(Potts)g(mo)-66
b(del)350 b(on)g Ft(Z)43269 8429 y Fs(2)43795 8911 y
Fx(,)334 b(Nucl.)10566 10516 y(Ph)-36 b(ys.)434 b(B)g
Fh(644)p Fx([FS],)g(495{508)i(\(2002\).)4317 13228 y([D])4534
b(R.)338 b(L.)g(Dobrushin,)357 b FA(Estimates)376 b(of)h
(semi{invariants)d(for)j(the)f(Ising)g(mo)-66 b(del)10566
14833 y(at)401 b(low)g(temp)-66 b(er)g(atur)g(es)p Fx(,)376
b(Amer.)364 b(Math.)f(So)36 b(c.)364 b(T)-108 b(ransl.)364
b Fh(177)p Fx(,)378 b(59{81)365 b(\(1996\).)4317 17545
y([D)-36 b(W])3234 b(K.)447 b(Druhl)e(and)h(H.)g(W)-108
b(agner,)449 b FA(A)-33 b(lgebr)-66 b(aic)475 b(formulation)g(of)h
(duality)g(tr)-66 b(ans-)10566 19150 y(formation)464
b(for)g(ab)-66 b(elian)464 b(lattic)-66 b(e)463 b(mo)-66
b(del)p Fx(,)433 b(Ann.)g(Ph)-36 b(ys.)434 b Fh(141)p
Fx(,)h(225)f(\(1982\).)4317 21862 y([F1])4028 b(C.M.)539
b(F)-108 b(ortuin,)564 b FA(On)d(the)g(r)-66 b(andom{cluster)561
b(mo)-66 b(del)561 b(II:)f(The)h(p)-66 b(er)g(c)g(olation)10566
23468 y(mo)g(del)p Fx(,)434 b(Ph)-36 b(ysica)434 b Fh(58)p
Fx(,)g(393{418)i(\(1972\).)4317 26180 y([F2])4028 b(C.M.)798
b(F)-108 b(ortuin,)886 b FA(On)799 b(the)g(r)-66 b(andom{cluster)798
b(mo)-66 b(del)798 b(III:)f(The)i(simple)10566 27785
y(r)-66 b(andom{cluster)465 b(mo)-66 b(del)p Fx(,)433
b(Ph)-36 b(ysica)434 b Fh(59)p Fx(,)g(545{570)i(\(1972\).)4317
30497 y([FK])3667 b(C.M.)540 b(F)-108 b(ortuin,)564 b(P)-108
b(.W.)539 b(Kasteleyn,)566 b FA(On)561 b(the)g(r)-66
b(andom{cluster)561 b(mo)-66 b(del)561 b(I:)10566 32102
y(Intr)-66 b(o)g(duction)587 b(and)i(r)-66 b(elation)588
b(to)h(other)f(mo)-66 b(dels)p Fx(,)603 b(Ph)-36 b(ysica)569
b Fh(57)p Fx(,)603 b(536{564)10566 33707 y(\(1972\).)4317
36419 y([FK)-36 b(G])2682 b(C.M.)310 b(F)-108 b(ortuin,)333
b(P)-108 b(.W.)310 b(Kasteleyn,)335 b(J.)309 b(Ginibre,)334
b FA(Corr)-66 b(elation)349 b(ine)-66 b(qualities)10566
38024 y(on)419 b(some)h(p)-66 b(artial)66 b(ly)419 b(or)-66
b(der)g(e)g(d)418 b(sets)p Fx(,)395 b(Comm)-36 b(un.)384
b(Math.)g(Ph)-36 b(ys.)384 b Fh(22)p Fx(,)395 b(89{103)10566
39629 y(\(1971\).)4317 42341 y([G])4506 b(R.B.)698 b(Gri\261ths)e
FA(Corr)-66 b(elations)706 b(in)h(Ising)e(ferr)-66 b(omagnets)706
b(II)p Fx(,)696 b(J.)i(Math.)10566 43946 y(Ph)-36 b(ys.)434
b Fh(8)g Fx(484{489)i(\(1967\).)4317 46658 y([Gr])4000
b(G.)648 b(Grimmett,)701 b FA(Potts)662 b(mo)-66 b(dels)662
b(and)g(r)-66 b(andom{cluster)661 b(pr)-66 b(o)g(c)g(esses)662
b(with)10566 48263 y(many{b)-66 b(o)g(dy)464 b(inter)-66
b(actions)p Fx(,)431 b(J.)j(Stat.)g(Ph)-36 b(ys.)433
b Fh(75)p Fx(,)i(67{121)g(\(1994\).)4317 50976 y([Gra])3350
b(S.)434 b(B.)g(Gra)-36 b(y)-108 b(,)433 b(I.E.E.E.)i(T)-108
b(rans.)433 b(Comp.)h Fh(20)p Fx(,)h(551,)g(\(1971\).)4317
53688 y([Gri])3639 b(G.)434 b(Grimmett,)f FA(Per)-66
b(c)g(olation)p Fx(,)432 b(Springer,)h(2nd)g(edition)g(\(1999\).)4317
56400 y([Ha])3902 b(H.)377 b(Hadwiger,)389 b FA(V)-100
b(orlesungen)428 b(\304)-681 b(ub)-66 b(er)412 b(Inhalt,)421
b(Ob)-66 b(er\260\304)-664 b(ache)412 b(und)g(Isop)-66
b(erime-)10566 58005 y(trie)p Fx(,)433 b(Springer,)g(1957.)4317
60717 y([HK])3541 b(J.)370 b(Hoshen)f(and)f(R.)i(Kop)36
b(elman,)383 b FA(Per)-66 b(c)g(olation)404 b(and)i(cluster)g
(distribution.)10566 62322 y(I.)636 b(Cluster)h(multiple)f(lab)-66
b(eling)636 b(te)-66 b(chnique)635 b(and)h(critic)-66
b(al)635 b(c)-66 b(onc)g(entr)g(ation)10566 63927 y(algorithm)p
Fx(,)433 b(Ph)-36 b(ys.)434 b(Rev.)h(B)e Fh(14)p Fx(,)i(3438)f
(\(1976\).)25253 70015 y(27)p eop
%%Page: 28 28
28 27 bop 4317 7306 a Fx([HKW])2205 b(A.)390 b(Hin)-36
b(terman,)398 b(H.)389 b(Kunz,)398 b(and)389 b(F.Y.)h(W)-108
b(u,)398 b FA(Exact)424 b(r)-66 b(esults)424 b(for)g(the)g(Potts)10566
8911 y(mo)-66 b(dels)465 b(in)f(two)h(dimension)p Fx(,)432
b(J.)i(Stat.)g(Ph)-36 b(ys.)434 b Fh(19)p Fx(,)g(621{632)i(\(1978\).)
4317 11623 y([KLMR])1554 b(R.)496 b(Kotec)-36 b(k)18
b(\266)-668 b(y,)512 b(L.)496 b(Laanait,)511 b(A.)496
b(Messager,)511 b(and)495 b(J.)h(Ruiz,)511 b FA(The)522
b Fu(q)48 b FA({states)10566 13228 y(Potts)398 b(mo)-66
b(del)397 b(in)f(the)h(standar)-66 b(d)397 b(Pir)-66
b(o)g(gov-Sina)-133 b(\304)-531 b(\263)395 b(the)-66
b(ory:)563 b(Surfac)-66 b(e)396 b(tension)10566 14833
y(and)465 b(Wilson)f(lo)-66 b(ops)p Fx(,)435 b(J.)f(Stat.)f(Ph)-36
b(ys.)434 b Fh(58)p Fx(,)g(199)h(\(1990\).)4317 17545
y([KP])3631 b(R.)402 b(Kotec)-36 b(k)18 b(\266)-668 b(y)402
b(and)e(D.)i(Preiss,)408 b FA(Cluster)435 b(exp)-66 b(ansion)433
b(for)i(abstr)-66 b(act)434 b(p)-66 b(olymer)10566 19150
y(mo)g(dels,)433 b Fx(Comm)-36 b(un.)433 b(Math.)h(Ph)-36
b(ys.)434 b Fh(103)p Fx(,)g(491)h(\(1986\).)4317 21862
y([KS])3793 b(R.)312 b(Kotec)-36 b(k)18 b(\266)-668 b(y)313
b(and)e(S.)g(Shlosman,)336 b FA(First)352 b(or)-66 b(der)352
b(phase)i(tr)-66 b(ansitions)350 b(in)i(lar)-66 b(ge)10566
23468 y(entr)g(opy)464 b(lattic)-66 b(e)463 b(systems,)434
b Fx(Comm)-36 b(un.)433 b(Math.)g(Ph)-36 b(ys.)434 b
Fh(83)p Fx(,)g(493)h(\(1982\).)4317 26180 y([LM])3522
b(J.)400 b(L.)f(Leb)36 b(o)-36 b(witz)399 b(and)g(A.)h(Martin-L\304)
-650 b(of,)406 b FA(On)433 b(the)g(uniqueness)g(of)g(the)g(e)-66
b(qui-)10566 27785 y(librium)559 b(state)h(for)g(ising)f(spin)h
(systems,)i Fx(Comm)-36 b(un.)537 b(Math.)h(Ph)-36 b(ys.)537
b Fh(25)p Fx(,)10566 29390 y(276)435 b(\(1972\).)4317
32102 y([LMMRS])650 b(L.)507 b(Laanait,)527 b(S.)507
b(Miracle-Sol)-36 b(\266)-614 b(e,)526 b(A.)507 b(Messager,)527
b(J.)507 b(Ruiz,)526 b(and)507 b(S.)g(Shlos-)10566 33707
y(man,)777 b FA(Interfac)-66 b(es)716 b(in)g(the)h(Potts)h(mo)-66
b(del)717 b(I:)f(Pir)-66 b(o)g(gov-Sinai)715 b(the)-66
b(ory)717 b(of)10566 35312 y(the)352 b(F)-100 b(ortuin-Kasteleyn)350
b(r)-66 b(epr)g(esentation)p Fx(,)333 b(Comm)-36 b(un.)311
b(Math.)f(Ph)-36 b(ys.)311 b Fh(140)p Fx(,)10566 36917
y(81{91)435 b(\(1991\).)4317 39629 y([LMeR])1987 b(L.)632
b(Laanait,)681 b(A.)632 b(Messager,)682 b(J.)632 b(Ruiz,)682
b FA(Disc)-66 b(ontinuity)644 b(of)j(the)f(Wilson)10566
41234 y(string)370 b(tension)f(in)g(the)h(4-dimensional)g(lattic)-66
b(e)368 b(pur)-66 b(e)371 b(gauge)f(Potts)h(mo)-66 b(del)p
Fx(,)10566 42839 y(Comm)-36 b(un.)434 b(Math.)f(Ph)-36
b(ys.)434 b Fh(126)p Fx(,)g(103{131)i(\(1989\).)4317
45551 y([Le])4136 b(S.)304 b(Lefsc)-36 b(hetz,)329 b
FA(Intr)-66 b(o)g(duction)344 b(to)h(T)-100 b(op)-66
b(olo)g(gy)p Fx(,)330 b(Princeton)303 b(Univ)-36 b(ersit)g(y)304
b(Press,)10566 47156 y(Princeton,)434 b(1942.)4317 49869
y([M])4335 b(S.)401 b(Miracle-Sol)-36 b(\266)-614 b(e,)409
b FA(On)435 b(the)g(c)-66 b(onver)g(genc)g(e)431 b(of)k(cluster)g(exp)
-66 b(ansion)p Fx(,)407 b(Ph)-36 b(ysica)10566 51474
y Fh(A)499 b(279)p Fx(,)434 b(244-249)h(\(2000\).)4317
54186 y([MM])3143 b(A.)533 b(Messager)h(and)e(S.)h(Miracle-Sol)-36
b(\266)-614 b(e,)558 b FA(Equilibrium)d(states)i(of)e(the)h(two-)10566
55791 y(dimensional)386 b(Ising)h(mo)-66 b(del)387 b(in)f(the)i
(two-phase)g(r)-66 b(e)g(gion)p Fx(,)365 b(Comm)-36 b(un.)349
b(Math.)10566 57396 y(Ph)-36 b(ys.)434 b Fh(40)p Fx(,)g(187{196)i
(\(1975\).)4317 60108 y([MW])2999 b(K.)591 b(R.)g(Mec)-36
b(k)g(e)590 b(and)g(H.)h(W)-108 b(agner,)630 b FA(Euler)609
b(Char)-66 b(acteristic)607 b(and)i(R)-66 b(elate)g(d)10566
61713 y(Me)g(asur)g(es)650 b(for)g(R)-66 b(andom)650
b(Ge)-66 b(ometric)649 b(Sets)p Fx(,)685 b(J.)636 b(Stat.)f(Ph)-36
b(ys.)636 b Fh(64)p Fx(,)686 b(843,)10566 63318 y(\(1991\).)25253
70015 y(28)p eop
%%Page: 29 29
29 28 bop 4317 7306 a Fx([M1])3685 b(K.)369 b(R.)g(Mec)-36
b(k)g(e,)381 b FA(Applic)-66 b(ations)404 b(of)g(Minkowski)g(F)-100
b(unctionals)405 b(in)f(Statistic)-66 b(al)10566 8911
y(Physics)p Fx(,)417 b(in)412 b(:)567 b FA(Statistic)-66
b(al)443 b(Physics)i(and)g(Sp)-66 b(atial)444 b(Statistics.)e(The)j(A)
-33 b(rt)444 b(of)10566 10516 y(A)-33 b(nalyzing)594
b(and)i(Mo)-66 b(deling)594 b(Sp)-66 b(atial)595 b(Structur)-66
b(es)595 b(and)h(Pattern)f(F)-100 b(orma-)10566 12121
y(tion)p Fx(,)499 b(Lecture)485 b(Notes)i(in)f(Ph)-36
b(ysics)487 b Fh(554)p Fx(,)500 b(K.)487 b(R.)g(Mec)-36
b(k)g(e)486 b(and)g(D.)h(Sto)-36 b(y)g(an)10566 13726
y(Eds.)434 b(Springer)e(\(2000\).)4317 16438 y([M2])3685
b(K.)527 b(R.)g(Mec)-36 b(k)g(e,)550 b FA(Complete)f(F)-100
b(amily)550 b(of)g(F)-100 b(r)-66 b(actal)550 b(Dimensions)f(Base)-66
b(d)551 b(on)10566 18043 y(Inte)-66 b(gr)g(al)463 b(Ge)-66
b(ometry)p Fx(,)433 b(submitted)f(to)i(Ph)-36 b(ysica)434
b(A)f(\(2000\).)4317 20756 y([O])4515 b(B.)470 b(L.)f(Okun,)478
b FA(Euler)499 b(Char)-66 b(acteristic)495 b(in)i(Per)-66
b(c)g(olation)497 b(The)-66 b(ory)p Fx(,)478 b(J.)470
b(Stat.)10566 22361 y(Ph)-36 b(ys.)434 b Fh(59)p Fx(,)g(523,)h
(\(1990\).)4317 25073 y([Or])4009 b(O.)655 b(Ore,)711
b FA(The)669 b(F)-100 b(our-Color)670 b(Pr)-66 b(oblem)p
Fx(,)710 b(Academic)656 b(Press,)711 b(New-Y)-108 b(ork,)10566
26678 y(London,)433 b(1967.)4317 29390 y([PV])3667 b(C.-E.)591
b(P\257ster)e(and)g(Y.)i(V)-108 b(elenik,)629 b FA(R)-66
b(andom)608 b(cluster)h(r)-66 b(epr)g(esentation)606
b(of)10566 30995 y(the)465 b(Ashkin-T)-100 b(el)66 b(ler)464
b(mo)-66 b(del)p Fx(,)433 b(J.)h(Stat.)g(Ph)-36 b(ys.)433
b Fh(88)p Fx(,)i(1295{1331)h(\(1997\).)4317 33707 y([S])4804
b(L.)817 b(A.)f(San)-36 b(tal\265)-650 b(o,)913 b FA(Inte)-66
b(gr)g(al)815 b(Ge)-66 b(ometry)815 b(and)i(Ge)-66 b(ometric)815
b(Pr)-66 b(ob)g(ability)p Fx(,)10566 35312 y(Addison-W)-108
b(esley)g(,)434 b(\(1976\).)4317 38024 y([Se])4226 b(J.)434
b(Serra,)g FA(Mathematic)-66 b(al)463 b(Morpholo)-66
b(gy)p Fx(,)434 b(Academic)g(Press,)g(\(1982\).)4317
40736 y([SyEs])2720 b(M.)462 b(F.)f(Syk)-36 b(es)462
b(and)f(J.)h(W.)g(Essam,)468 b FA(Exact)491 b(Critic)-66
b(al)488 b(Per)-66 b(c)g(olation)489 b(Pr)-66 b(ob)g(a-)10566
42341 y(bilities)430 b(for)g(Site)g(and)h(Bond)h(Pr)-66
b(oblems)431 b(in)f(Two)i(Dimensions)p Fx(,)402 b(J.)c(Math.)10566
43946 y(Ph)-36 b(ys.)434 b Fh(5)p Fx(,)g(1117-1121,)i(\(1964\).)4317
46658 y([W)-108 b(a1])2999 b(H.)306 b(W)-108 b(agner,)331
b FA(Euler)348 b(Char)-66 b(acteristic)345 b(for)i(A)-33
b(r)-66 b(chime)g(de)g(an)344 b(L)-66 b(attic)g(es)p
Fx(,)329 b(\(2000\).)10566 48263 y(\(unpublished\))4317
50976 y([W)-108 b(a2])2999 b(K.)307 b(R.)f(Mec)-36 b(k)g(e)306
b(Th.)g(Buc)-36 b(hert)305 b(and)h(H.)g(W)-108 b(agner,)332
b(Astron.)306 b(Astroph)-36 b(ys.)306 b Fh(288)p Fx(,)10566
52581 y(697,)435 b(\(1994\).)25253 70015 y(29)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF