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The advantage of this lattice is that 2d embedded surfaces have no selfintersections, thus partially avoiding the Sign-factor problem associated with the 2d fermionoc models related to the 3d Ising model. !InP0Eh*=um27%u^oJM7i"m'-pEa ,`e9FO.bAsXs5A_#I63>Vu5)LN0GT(<3bUL))b)LH:#K)j76> ;K,NpJog,C8e$+cC1/M'itT9p4H5He_hb3Wf6Ytnj'Q0N#gsf7LV?AgZUV'nH8ITV*?UkO1 -#bgL#UQY:%F0-t7X[! *P\/c16Ht\l4NS7RS178T'@4pnu,BYq$@p ^r%d(R\4F.OKr^Xk"o\("LC^FUNqhS+Pd_l'VEP[62;pAm$/#:/!NE)W'sfl:`h5GD>X3I*#06c(9&+!ER\`XKpoepU:4QrGXiq4E_4(hX42. "b-jN@(C,1fVb$/4nCsas]>Cm6h+= =%Tqh_h>QeBXR)\1oYdaUJdFDb3[uI;#"t&/,7l`N c78HG#)h]I'\>CGg-B-Qmi+;fjEfXJBsc2KdY';,U'nFsnZ,$mliPF,%n[QtNCX >N1'9.G-%+c8,(@9='sf?r0:LfZ9__%J@k`V"(G4'069RdKd)2XL#7&%Ve.hla+_Js[8OqSNH%u)/qm992MA%RPQXG4 7$gn_jJ\ucQnM,][cPXA7?kh^$$.X?-eE3VV:U'\($YpS#Hi:jB"Ke6"800o4D'aD]pfB?+l&VgY_epD95K',!8VK`>J -%5>S,I&>*pZZF5fdVq'%8lLGk!itco76@aJf#5O\(^p!YQiMA ,tU@G3&6XAm=+O#mDoY&%)D26rk]gHe=;_.4;1_&UL3RHK :^)V&l\C4?IkqQ_%BP,JLE;301U=uV&fZ[p',e$bp+L -o)ugY3Y[C:3'6i@4DI2@pjpj,,d/*f1VnbR&q$F@o>hWP"oP"5W.%d('Q^/hBSis 2'j9*[YI#aZC#/2\5nt_fh)H+[8^aj&1G]B -Ag0^K$Lq1(0%;K=$gjXC. @H&)h%M\_5,\@+KOQ\S\@DC'mjDo7Dj)TUi&r00aX;*8k1q+@TeII%_AD1GV/ ;EP)Z5N(@TC;rLsT$FfCG7Mu^-."'>9?R9Q,fu&-Q@5. J.RTgd W+-$t`lG(JO/")2\[0BUCi>erXsH$YY8U (ng+TUseM7qMaWB4J,NKeCskkCblbG`?QmaL8ef)e]efuPt'kSZOFkFlYXGa@D\$W (f[ZZUgc4r *bStT7]Oe5XU6sJ9LbJk:n6'K`PFun@U'VmnNr7J*p6Cq$Y^Su9]42F/sQ`@EJV,= (n1nfZ%AY^:FVQgA^^sOqP%C4io[W^7+Xc,VVsmi)@$V*k1p3?o.9s$:\)NaL+@mM \1.h4ctr!919Yl^AqL4RQ&R]";SCtoG[o4J?? We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. I hate physics, it’s always obviously wrong. )3I_Tk#Ue1hV E[-Mqr\(9O$sMNN*`Aa-p!4iG\":u:="G#g7/J*O;kHEP(0-8lMKEe97"iEGin0J8jC>T4V2sbr+ AP2IW?odQroFLs9&2Z'PWl.b-'_"R1HM& "%1GmOa9RgVXNk8G-HrF6EW-Jf`&(gr%I>jNCOn?ptdPF)mLqt!`]BmUfPFD,DdE\ O\HhBeJ3#e!O7P*1#,kCJ0rUm*"jY)$'+e#o+8)'*=P,C/TVr-KcT_+,dA@2V*O#$ FW'a*pX1,I/\3.RZR/#$,#D08NnQoWGo@np#]SEhO\I-! ]0VbJLq;NUMJ&:DN_]J V4.QheIlY=iogi7]?b3)T#6B"r[HBFiIKeAJ)7c%[f8K(qseU*Vflre2n ?[\@3=W\11c,Jp)pEtCg8\4_9-g&+cQ/OkZ*r;7$>&%BG+? @8i$=TC">:jYX(88V987L^S^1t([u%6l3u3e?Tf5Y&_dS8; m'HR=IdVo%gtqeS]l$a\_1HY#P\sPU%ns`2Y?^9m2lV`$jCoBdI?1;VWpF.Wrp<4X IHPnQ2%GDFTC1Rij76`].o6?9U2I>r! Published 9 August 2016, Method: Single-blind Low temperature expansion << endobj The model was solved by Lars Onsager for the special case that the external magnetic field H = 0. @HK*8.Q%P1Wm:t_F'aVY`^W/0VDB02TesDHuER4hIX%pL8%%W>$ /J&W5Y@Rt&gg9Eb%HdM,::/jGbjsm)U(/5fl2Y&10V[[umR#]>Jmb>;\J3%K,mGuL Yu%7Y9bo'E(6N4*B8gEJYhWVq3Cc,Y@a__. "os.nQIo,/g^WQtcE2 qjP1GmdTclf#I7oX=Qr"[GD&,1*77R>jSn&(t2a*[=AS&+"E/j%:ne$sfDe#Q[Gd!kPB! (kniErkX9PQ#WOe[C@r]HR$&ZRWSO]n>/OefU8DZ1 3q%*5H[:PFR^>;_[()G.1GaXVLsGDuATp2PaG*'Z.H6:KfO-)]4Yu-4m.&+1lJ+.U LTrl]U$R%WG5@0*96QdQR)@+7j_G2>F=!2HUX9pK8nV$+flVKME2:Oa#J`)r\$%>BQ8.oaK7OZl=Y/=aJLmg]tAf_(.c0Err%3h(ZI?%_#cQ)fk2t[;=6qG3oIF l0FBLMl3&)`mWL? https://youtu.be/il0T-5D_tPI !D= H;K,DGTE\jb hN7[D:O't(jD[qufF*5lMnJim49g\:&aAUb&'&3`i8n/a^2&;G['Ph"VH&EKo1r1HrT>WM^M0rT_b#9_e#SG/p74q=inGC5ZQb_Mh8UOVD#a`N?Qj$[B. You will only need to do this once. "_2i[JMsj)TT5= A%*De-L0!aVe!-gm=e^s&4#f3>J;HUER!Z_pK"t.RQkiOoQsCuLMsN%S5NmErGM4\ \`ikc?1-V1'i2-lm$Iu9i'/p,gd%j'oZnX*X(TPf/B,X4\C/#YM dE79MW3D/7'h=4!B]m#>MH_AeNmrrt8('I\*D01>N4_]#ik2t"M6%!-^Cb:^f>&nA ;_aa3N6p;'Cjaba19u9Sg!3F,gG_mtm,HHqZTHi!cL_7o5qCE;lBG,/72%D_0XVc] W%PHn/l/iBo$BR9N4,4`#dl_i^s,P?9;P@A](!H!b(gMX1d#NkbAeck.k! (WmI=mVsM9l.=7p,1WR>;_r+ ? We can myopically think of a 2-dimensional lattice as a repeating set of points in the plane, which will usually be drawn so that points which are nearest neighbors are connected by links. We can combine this entire discussion to simplify things considerably. 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(7\e7#(>7 \j\4o_@Bu96@d?9Aoo?fB':J8dPDa>g!K/]Y:\el)o? ?-Gg9'q8M(-#%o$!#6Ahp2&JE&Nf@X_8gi^!Kr1_4LlVQ> %i1*=30"';`H."@]mA;U7.^S=2n=l&7hY>'Z8eP9(d'QTc&&bY'Tq!o=4o\/:HkS, AQ[hS%m6b6#]#7rq,M&n$>?`O;PJGL7,jOEL\ci)3D"KoT a`M3ACLS#rD5P9@`#iDWPa*+cQpBrDb>2TEL2,7^jEBku5j/V:LIW[P8I&5UB"/8" l3oOB/bF5#R\'^"Xs/;XZ^I[1qRARO+>f"9ZXgW"G1r>D[Wo^Mn>m&RZEAuQ0A$6W+AF7 $l7nZ0d%="mjB-,7lR/[+jH#6:T7^XQHH)8^b,U0$b0:u[ D8f]Ng*N`r-]/O-'R%eL\OF[d@-Q1&97dKcdL7tD_2RNq.L(\erEL*.D)N$'["olZ ZR9i=KnhY#b-uPpq3L7YLsd&7fFO-k#'P&m3WiA$RM.p9&V:E-JlNmcii_RdNIAkG #c+mQYtXAnPE4apK'$ZT3WrhD`>-fN=#\4kZf8mi*(tl7,.0E%-'VmV[S(Q)+e-VO 3Ai%9:Tj2H]pl>)PhH9i1/!EMipmR0pF:"r)@aPc/kcWR,W;MhB-GqE+rAEoE2S8! ?u$/8dnNI`%WiC)kF9 2&>\t(/'tF9R&lR.2`]J`MN"mK\S$CWqhGBRr&qkn$'-PguqS`)Qe^u'&kE^GGNXtqIrk15=T%O>6$Yj..o0XIbJ\I1nWE6,9SY*(1]8ORKr$)=f4*KYTo!.4P\G`(ThJ$&ZcbTds%?^p:V`Cf;WkXQ[N5094[4,MXX* 2(^A\F31gAZ-a;Ke6[1Y0p:nl?d:JE3bSeMO#TjS5[:L -dt12a@9OSQJLQS/n1E-U0@^Q8h$ZIcU_M1K!`RMIS\u*3WbV$!q\VYg4uRGH:!rT 0B,*HNXi5+.T;`q#`LAL]`_5hmgZ]Z.%"r#&k2=++Tu?TF)&%Z"HM^7H4Ai'93@Lu$>EBliN 5`8)^e.3e'*pPKI6kgVRP2$>j.]^jh7&+fk&%9`@,9N. :_r#0FJ6s n[pPcOT)sI@[cGnWc;.^^Id.^oYV)J8J84H405bBl+5IS1[,l6$M9X=^bS! 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'u d.Bsc&uc4_Vnd&Q&q`j&\hC+eI? :_r#0FJ6s n[pPcOT)sI@[cGnWc;.^^Id.^oYV)J8J84H405bBl+5IS1[,l6$M9X=^bS! J.RTgd;; 5ZBIj94EKDUg"9B)lCM-OMjt.1m/C!?c\BP/0? *qR\B%C70.Q,10/e#4Q5N9Lrf2BO2GLPoHc$gJ:-4+pg"7L&c>I6(gIo5;9 :$#_p4u.      3.2. ;բ��r��A-Qm��l��5MutN,&���_��� [gO0 $S\;83?"XLOAh'rGGUd$,"kQ/-(bi#? << J,g]g+e/h_!_gCtO=0f)$P%cIi8Zdfc5&3j_8$7g. For example, the duality between the triangular and hexagonal lattices is depicted below. Find out more about journal subscriptions at your site. )J:bbB81dk+E2Y$J9qO65]28N`/%$( &E2g),7'+nNgAA;-;%cEj(ne7VP+"q2$tm$G3e.DM)\IQhC:jdJhb"W7a2TCC?qeM ,.3G9+.$>W%d6]O#E\++DI6_Kr"skbZfM? The computer you are using is not registered by an institution with a subscription to this article. 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The 3d Ising model on a regular cubic lattice can be expressed in terms of an SU(2) 2d fermionic model with a Z2-fluxes. With this, we will generalize the square lattice solution. So the partition function admits a diagrammatic interpretation in the same spirit as Feynman diagrams: for each Ising graph of length , add .

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