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Additional resources for Statistical Mechanics of Periodic Frustrated Ising Systems
Example text
Effective two spins tral Transformations restricted all c a s e s , three . last sum exactly and . (see Fig. pendent We . 2K simple , the in- decorated be i n v e r t e d . How- in a c h a i n w i t h o u t occur. can b e g e n e r a l i z e d field (ref. 34), as to s e v e r a l long as it spins. transformation transformation. " _ K~ K~ K3 (b} (c) y K23 Fig. 3 Decimation transformations: (a) Decoration-iteration transformation, (b) star-triangle transformation, (c) star-square transformation. 2b S~a~zTEian~le Transformation This t r a n s f o r m a t i o n is completely analog to the d e c o r a t i o n - i t e r a t i o n transformation, only the i n t e r m e d i a t e spin or group of spins is now i n t e r a c t i n g w i t h three other spins.
The in all and function distance that the GS however, Tc = O frusAs and . the three . This diverges frustration system are I/2 class. length the there entropy D = shows , and general, I/2 odd Tc = O A F o) T > 0 T = O GS universality T = 0 . In For . For is value with (point LRO the distance correlation transition interactions (-r/~(T)) Ising interaction correlation with even a different , the the chains with usual T = O a phase inhibit finite perties G(r) this ones strong Therefore, . Thus the system the nn-directions (~r/2) for of chains.
Vaks and gular J3 Geilikman Ising = J + 6 43 system , J have near < O , r61 studied the << the frustration IJi . ) 6 < O : the GS shows Id L R O In Fig. 14 dashed the specific line for heat 6 < O c(T) . is ; T c # 0 only; shown as ; Tc = 0 full line for 6 > O 49 T Fig. 14 As Specific heat of the anisotropic AF triangular lattice (J1 = J 2 = J3 - ~ , I~I << IJil) For ~ > O (full curve) there is a logarithmic divergence, not for ~ < 0 (dashed curve). (after ref. 43). expected T >> 161 c the = is Ising transition t -3/2 6 < O the maximum at occurs at only of occurs and are broken with the weaker ones.