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b(on)f(the)h(lo)r (cal)f(slop)r(e)h Fd(u)g Fr(=)h Fj(r)p Fk(h)p Fr(.)61 b(Belo)n(w)35 b(the)h(roughening)-150 913 y(transition)25 b Fk(f)34 b Fr(has)25 b(a)g(cone)g(at)h Fd(u)d Fr(=)f(0)j(and)h(for)f (small)g Fd(u)h Fr(b)r(eha)n(v)n(es)-150 1013 y(as)400 1180 y Fk(f)9 b Fr(\()p Fd(u)p Fr(\))591 1158 y Fj(\030)591 1184 y Fr(=)678 1180 y Fk(\015)c Fr(\()p Fk(\022)r Fr(\))p Fj(j)p Fd(u)p Fj(j)19 b Fr(+)f Fk(B)t Fr(\()p Fk(\022)r Fr(\))p Fj(j)p Fd(u)p Fj(j)1303 1146 y Fi(3)1745 1180 y Fr(\(14\))-150 1347 y(with)33 b Fk(\022)j Fr(the)d(p)r(olar)f(angle)g (of)h Fd(u)g Fr([18)o(].)53 b(The)33 b(line)g(sti\013ness)h Fe(e)-47 b Fk(\015)38 b Fr(is)-150 1446 y(de\014ned)32 b(through)f Fe(e)-47 b Fk(\015)5 b Fr(\()p Fk(\022)r Fr(\))30 b(=)f Fk(\015)5 b Fr(\()p Fk(\022)r Fr(\))21 b(+)f Fk(\015)1041 1416 y Fq(00)1083 1446 y Fr(\()p Fk(\022)r Fr(\).)49 b(As)32 b(argued)e(in)h([19)o(])-150 1546 y(for)38 b(short)f(range)g(surface)g(mo)r(dels)h(the)g(Gaussian)f(curv)-5 b(ature)-150 1646 y(det)14 b 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Fr(is)h(the)f(La-)-150 2255 y(grange)24 b(m)n(ultiplier)h(adjusted)h (so)f(to)g(giv)n(e)g(the)h(correct)e(v)n(olume.)-150 2354 y Fk(h)33 b Fr(is)h(con)n(v)n(ex)e(do)n(wn)n(w)n(ards)f(and)i(has) g(a)g(con)n(v)n(ex)f(facet)h(lying)g(in)-150 2454 y(the)24 b Fk(x)p Fr(-)p Fk(y)j Fr(plane.)35 b(The)24 b(facet)g(b)r(oundary)f (is)g(determined)h(b)n(y)g Fk(\015)5 b Fr(\()p Fk(\022)r Fr(\))-150 2554 y(alone.)73 b(Close)39 b(to)h(the)g(facet)g(edge,)j Fk(h)1171 2531 y Fj(\030)1171 2558 y Fr(=)1279 2554 y Fj(\000)1354 2521 y Fi(2)p 1354 2535 34 4 v 1354 2582 a(3)1397 2554 y Fk(\015)1440 2566 y Fh(P)9 b(T)1543 2554 y Fk(d)1586 2523 y Fi(3)p Fh(=)p Fi(2)1731 2554 y Fr(with)-150 2653 y Fk(d)37 b Fr(the)g(normal)f(distance)g(to)h(the)g(facet)f(edge,) j(whic)n(h)d(de\014nes)-150 2753 y(the)29 b(P)n(okro)n(vsky-T)-7 b(alap)r(o)n(v)22 b(co)r(e\016cien)n(t)28 b Fk(\015)1146 2765 y Fh(P)9 b(T)1250 2753 y Fr(.)38 b(Under)28 b(Legendre)-150 2852 y(transformation)35 b(the)i(angle)f Fk(\022)k Fr(b)r(ecomes)c(the) h(angle)f(b)r(et)n(w)n(een)-150 2952 y(the)29 b Fk(x)p Fr(-axis)g(and)g(the)g(outer)g(normal)f(to)h(the)g(facet)g(and,)g (corre-)-150 3052 y(sp)r(ondingly)-7 b(,)27 b Fk(\015)329 3064 y Fh(P)9 b(T)433 3052 y Fr(,)27 b(the)h(lo)r(cal)f(curv)-5 b(ature)27 b Fk(\024)p Fr(,)g(and)h(the)g(distance)-150 3151 y Fk(r)35 b Fr(of)e(a)f(p)r(oin)n(t)g(on)g(the)h(edge)f(to)g(the)h (origin)e(are)h(parametrized)-150 3251 y(through)27 b(this)h(angle)f Fk(\022)r Fr(.)37 b(The)28 b(relationship)f(b)r(et)n(w)n(een)h Fe(e)-47 b Fk(\015)33 b Fr(and)27 b Fk(B)-150 3351 y Fr(implies)555 3517 y Fk(\015)603 3483 y Fi(2)598 3538 y Fh(P)9 b(T)701 3517 y Fk(\024)23 b Fr(=)g(2)p Fk(`)937 3483 y Fq(\000)p Fi(2)1025 3517 y Fk(\031)1075 3483 y Fq(\000)p Fi(2)1164 3517 y Fk(:)558 b Fr(\(15\))-67 3684 y(W)-7 b(e)33 b(return)f(to)h(the)g(b)r(order)f(ledge)g(\015uctuations) g(close)g(to)h(a)-150 3784 y(giv)n(en)c(angle)f Fk(\022)326 3796 y Fi(0)364 3784 y Fr(.)43 b(F)-7 b(or)29 b(this)g(purp)r(ose)g(it) h(is)g(con)n(v)n(enien)n(t)e(to)i(cen-)-150 3884 y(ter)j(the)g Fk(x)p Fr(-)p Fk(y)j Fr(axis)c(co)r(ordinate)g(system)h(at)g Fk(r)r Fr(\()p Fk(\022)1371 3896 y Fi(0)1409 3884 y Fr(\))g(with)h(the) f Fk(x)p Fr(-)-150 3983 y(axis)28 b(tangen)n(tial)f(and)h(the)h Fk(y)s Fr(-axis)e(along)g(the)i(inner)f(normal)g(to)-150 4083 y(the)41 b(facet.)77 b(In)41 b(this)h(frame,)h(w)n(e)e(denote)g(b) n(y)g Fk(y)48 b Fr(=)c Fk(b)p Fr(\()p Fk(x)p Fr(\))e(the)-150 4183 y(\015uctuating)h(b)r(order)f(step.)83 b(Then)44 b Fj(h)p Fk(b)p Fr(\()p Fk(x)p Fr(\))p Fj(i)50 b Fr(=)1437 4150 y Fi(1)p 1437 4164 V 1437 4211 a(2)1480 4183 y Fk(\024)p Fr(\()p Fk(\022)1599 4195 y Fi(0)1636 4183 y Fr(\))p Fk(x)1715 4152 y Fi(2)1753 4183 y Fr(,)d(in)-150 4282 y(appro)n(ximation.)60 b(F)-7 b(or)36 b(su\016cien)n(tly)f(small)h Fj(j)p Fk(x)p Fj(j)p Fr(,)j(still)d(large)f(on)-150 4382 y(the)g(scale)e(of)h(the)h(lattice,)h Fk(b)p Fr(\()p Fk(x)p Fr(\))e(is)h(lik)n(e)e(a)h(random)f(w)n(alk)h(and)-150 4481 y(V)-7 b(ar)-21 4414 y Fe(\000)17 4481 y Fk(b)p Fr(\()p Fk(x)p Fr(\))11 b Fj(\000)g Fk(b)p Fr(\(0\))393 4414 y Fe(\001)454 4459 y Fj(\030)454 4486 y Fr(=)541 4481 y Fk(\033)591 4451 y Fi(2)629 4481 y Fj(j)p Fk(x)p Fj(j)p Fr(,)25 b(whic)n(h)f(de\014nes)g(the)g(lo)r(cal)f(w)n(ander-) -150 4581 y(ing)31 b(co)r(e\016cien)n(t)h Fk(\033)434 4551 y Fi(2)471 4581 y Fr(.)49 b(F)-7 b(ollo)n(wing)31 b([20)o(])g(it)h(is)g(natural)e(to)i(equate)-150 4681 y Fk(\033)s Fr(\()p Fk(\022)r Fr(\))5 4651 y Fi(2)71 4681 y Fr(with)c(the)g(in)n(v)n(erse)e(sti\013ness)j Fe(e)-47 b Fk(\015)5 b Fr(\()p Fk(\022)r Fr(\))1144 4651 y Fq(\000)p Fi(1)1234 4681 y Fr(.)-67 4780 y(This)28 b(implies)348 4947 y Fk(\033)398 4913 y Fi(2)458 4947 y Fr(=)23 b Fk(\024`;)179 b(\024)23 b Fr(=)g Fk(\031)1040 4913 y Fi(2)1077 4947 y Fk(\015)1125 4913 y Fi(2)1120 4968 y Fh(P)9 b(T)1224 4947 y Fk(\033)1274 4913 y Fi(4)1312 4947 y Fk(=)p Fr(2)349 b(\(16\))-150 5114 y(v)-5 b(alid)32 b(for)g(an)n(y)g(p)r(oin)n(t)h(on)f(the)h(facet)f(edge.)51 b(In)33 b(particular)e(the)-150 5214 y(shap)r(e)37 b(of)h(the)g(facet)f (edge)h(can)f(also)f(b)r(e)i(infered)g(from)f Fk(\033)s Fr(\()p Fk(\022)r Fr(\).)-150 5313 y(F)-7 b(or)28 b(the)h(Ising)f (corner)g(in)h(the)g([100]-[010])c(frame)k(one)f(obtains)-150 5413 y Fk(A)d Fr(=)e Fk(\033)75 5383 y Fi(2)113 5413 y Fr(\(1)c(+)f(tan)409 5382 y Fi(2)460 5413 y Fk(\022)r Fr(\))533 5383 y Fi(3)p Fh(=)p Fi(2)638 5413 y Fr(.)39 b(Th)n(us)28 b(in)h(the)g(tangen)n(tial)e(frame)h(the)2042 -83 y(scaling)e(form)i(\(13\))f(generalizes)f(to)2195 113 y(V)-7 b(ar)2324 46 y Fe(\000)2362 113 y Fk(b)p Fr(\()p Fk(x)p Fr(\))19 b Fj(\000)f Fk(b)p Fr(\(0\))2753 46 y Fe(\001)2814 91 y Fj(\030)2814 117 y Fr(=)2902 113 y Fk(\033)2952 79 y Fi(4)p Fh(=)p Fi(3)3057 113 y Fk(`)3092 79 y Fi(2)p Fh(=)p Fi(3)3196 113 y Fk(g)3239 46 y Fe(\000)3286 81 y Fi(1)p 3286 95 V 3286 142 a(2)3329 113 y Fk(\033)3379 79 y Fi(2)p Fh(=)p Fi(3)3484 113 y Fk(`)3519 79 y Fq(\000)p Fi(2)p Fh(=)p Fi(3)3675 113 y Fk(x)3722 46 y Fe(\001)3760 113 y Fk(:)154 b Fr(\(17\))2042 309 y(W)-7 b(e)31 b(emphasize)f(that)h (there)f(are)f(only)i(t)n(w)n(o)e(indep)r(enden)n(t)j(ma-)2042 409 y(terial)j(parameters,)i(whic)n(h)f(through)g(\(15\))g(and)g (\(16\))g(can)g(b)r(e)2042 509 y(reexpressed)26 b(in)i(terms)f(of)g Fk(\024)h Fr(and)f Fk(\015)3186 521 y Fh(P)9 b(T)3290 509 y Fr(.)2125 615 y(As)42 b(our)f(main)h(no)n(v)n(el)f(\014nding,)46 b(for)c(surface)f(mo)r(dels)h(with)2042 715 y(short)29 b(range)g(in)n(teractions,)h(the)g(b)r(order)g(ledge)g(of)g(a)f(facet)i (has)2042 814 y(\015uctuations)37 b(of)h(size)f Fk(`)2811 784 y Fi(1)p Fh(=)p Fi(3)2915 814 y Fr(.)67 b(Th)n(us)38 b(they)f(are)g(m)n(uc)n(h)h(reduced)2042 914 y(in)d(comparison)d(with)j (a)f(simple)h(random)f(w)n(alk)f(mo)r(del.)58 b(The)2042 1014 y(scaling)30 b(function)i Fk(g)i Fr(for)d(the)g(v)-5 b(ariance)30 b(of)i(the)f(\015uctuations)g(is)2042 1113 y(kno)n(wn)f(from)h(our)g(theory)-7 b(.)47 b(There)31 b(are)f(t)n(w)n(o)g(material)h(related)2042 1213 y(constan)n(ts.)i(Exp) r(erimen)n(tally)-7 b(,)20 b(w)n(e)g(exp)r(ect)f(that)h(at)g(least)f (the)h(re-)2042 1312 y(duction)25 b(of)h(the)f(\015uctuations)h(could)f (b)r(e)h(observ)n(ed.)34 b(W)-7 b(e)26 b(tested)2042 1412 y(this)h(prediction)g(on)g(the)h(single)e(sample)h(of)g(Figure)g (1)g(with)g(en-)2042 1512 y(couraging)32 b(results,)k(of)e(course)g(ha) n(ving)f(the)i(v)-5 b(aluable)34 b(adv)-5 b(an-)2042 1611 y(tage)35 b(that)h(the)g(surface)f(free)g(energy)g(in)h(kno)n(wn)f (ana)n(ytically)-7 b(.)p 2764 1752 598 5 v 2839 1753 449 7 v 2914 1754 299 9 v 2988 1755 150 11 v 2125 1963 a Fc(\003)2194 1995 y Fo(Electronic)27 b(address:)35 b Fb(ferrari@ma.tum.de)2128 2050 y Fc(y)2194 2082 y Fo(Electronic)27 b(address:)35 b Fb(praehofer@ma.tum.de)2128 2137 y Fc(z)2194 2169 y Fo(Electronic)27 b(address:)35 b Fb(spohn@ma.tum.de)2080 2256 y Fo([1])f(S.)26 b(Surnev,)f(P)-6 b(.)26 b(Co)r(enen,)h(B.)f(V)-6 b(oigtl\177)-38 b(ander,)27 b(H.)e(P)-6 b(.)26 b(Bonzel,)h(and)2194 2343 y(P)-6 b(.)26 b(Wyn)n(blatt,)f(Ph)n(ys.)h(Rev.)f(B)h Fa(56)p Fo(,)g(12131)i(\(1997\).)2080 2430 y([2])34 b(M.)28 b(No)n(wic)n(ki,)h(C.)f(Bom)n(bis,)g(A.)f(Em)n(undts,)f(H.)h(P)-6 b(.)27 b(Bonzel,)i(and)2194 2518 y(P)-6 b(.)26 b(Wyn)n(blatt,)f(Europh) n(ys.)h(Lett.)f Fa(59)p Fo(,)i(239)g(\(2002\).)2080 2605 y([3])34 b(M.)28 b(No)n(wic)n(ki,)h(C.)f(Bom)n(bis,)g(A.)f(Em)n(undts,) f(and)h(H.)g(P)-6 b(.)28 b(Bonzel,)2194 2692 y(preprin)n(t)d(\(2002\).) 2080 2779 y([4])34 b(V.)22 b(L.)h(P)n(okro)n(vsky)e(and)h(A.)g(L.)g(T) -6 b(alap)r(o)n(v,)24 b(Ph)n(ys.)e(Rev.)g(Lett.)g Fa(42)p Fo(,)2194 2866 y(65)27 b(\(1978\).)2080 2954 y([5])34 b(H.)26 b(Sp)r(ohn,)f(J.)h(Stat.)g(Ph)n(ys.)g Fa(47)p Fo(,)g(669)h(\(1987\).)2080 3041 y([6])34 b(D.)57 b(C.)g(Sc)n(hl\177) -38 b(o\031er,)65 b(L.)56 b(K.)g(V)-6 b(erheij,)65 b(G.)57 b(Rosenfeld,)64 b(and)2194 3128 y(G.)27 b(Comsa,)f(Ph)n(ys.)g(Rev.)f (Lett.)h Fa(82)p Fo(,)g(3843)h(\(1999\).)2080 3215 y([7])34 b(S.)26 b(V.)g(Khare)f(and)h(T.)g(L.)g(Einstein,)h(Ph)n(ys.)e(Rev.)h(B) g Fa(54)p Fo(,)g(11752)2194 3302 y(\(1996\).)2080 3389 y([8])34 b(S.)k(Karlin)h(and)e(G.)h(McGregor,)43 b(P)n(aci\014c)c(J.)g (Math.)f Fa(9)p Fo(,)k(1141)2194 3477 y(\(1959\).)2080 3564 y([9])34 b(F.)27 b(Dyson,)e(J.)h(Math.)h(Ph)n(ys.)e Fa(3)p Fo(,)h(1191)h(\(1962\).)2042 3651 y([10])34 b(T.)28 b(L.)e(Einstein)h(and)f(O.)h(Pierre-Louis,)h(Surf.)f(Sci.)f Fa(424)p Fo(,)i(L299)2194 3738 y(\(1999\).)2042 3825 y([11])34 b(T.)53 b(L.)e(Einstein,)59 b(H.)51 b(L.)h(Ric)n(hards,)58 b(S.)52 b(D.)f(Cohen,)58 b(and)2194 3912 y(O.)26 b(Pierre-Louis,)h (Surf.)f(Sci.)g Fa(493)p Fo(,)h(460)f(\(2001\).)2042 4000 y([12])34 b(J.)27 b(Villain)f(and)g(P)-6 b(.)26 b(Bak,)g(J.)g(Ph)n(ysique)f Fa(42)p Fo(,)h(657)h(\(1982\).)2042 4087 y([13])34 b(M.)40 b(Pr\177)-38 b(ahofer)41 b(and)d(H.)h(Sp)r(ohn,) j(J.)e(Stat.)f(Ph)n(ys.)g Fa(108)p Fo(,)44 b(1071)2194 4174 y(\(2002\).)2042 4261 y([14])34 b(C.)24 b(A.)e(T)-6 b(racy)23 b(and)g(H.)f(Widom,)h(Comm)n(un.)e(Math.)j(Ph)n(ys.)e Fa(159)p Fo(,)2194 4348 y(151)27 b(\(1994\).)2042 4435 y([15])34 b(A.)25 b(Ok)n(ounk)n(o)n(v)e(and)i(N.)g(Reshetikhin,)g(to)g (app)r(ear)g(in)g(J.)h(Amer.)2194 4523 y(Math.)h(So)r(c.,)f (arXiv:math.CO/0107056.)2042 4610 y([16])34 b(R.)e(Cerf)i(and)d(R.)h (Ken)n(y)n(on,)h(Comm.)f(Math.)g(Ph)n(ys.)g Fa(222)p Fo(,)j(147)2194 4697 y(\(2002\).)2042 4784 y([17])f(P)-6 b(.)56 b(L.)g(F)-6 b(errari)57 b(and)e(H.)h(Sp)r(ohn,)63 b(preprin)n(t,)f(arXiv:cond-)2194 4871 y(mat/0212456.)2042 4958 y([18])34 b(E.)25 b(E.)f(Grub)r(er,)g(W.)g(W.)g(Mullins,)i(J.)e (Ph)n(ys.)g(Chem.)f(Solids)h Fa(28)p Fo(,)2194 5046 y(875)j(\(1967\).) 2042 5133 y([19])34 b(Y.)h(Akutsu,)g(N.)f(Akutsu,)h(and)f(T.)h(Y)-6 b(amamoto,)35 b(Ph)n(ys.)g(Rev.)2194 5220 y(Lett.)26 b Fa(61)p Fo(,)h(424)f(\(1988\).)2042 5307 y([20])34 b(Y.)d(Akutsu)e(and)h(N.)g(Akutsu,)g(J.)h(Ph)n(ys.)g(A:)f(Math.)h(Gen.) f Fa(19)p Fo(,)2194 5394 y(2813)e(\(1986\).)p eop %%Trailer end userdict 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