Self-duality of the O(2) gauge transformation and the phase structure of vertex models

L. Šamaj and M. Kolesík

Physica A: Statistical Mechanics and its Applications, 1993, vol. 193, issue 1, 157-168

Abstract: For the symmetric two-state vertex model formulated on a lattice with an arbitrary coordination number q, we construct a variational series expansion of the free energy with a free gauge parameter playing the role of the variational variable. In the lowest order of the variational series expansion we obtain the Bethe approximation. Its analytical treatment provides a new method of searching for the self-dual manifolds for lattices of higher coordination number q and gives some information about the internal structure of the self-dual manifolds where the first- and second-order phase transitions take place. The results are systematically improved by considering higher-order terms in the variational series expansion.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:193:y:1993:i:1:p:157-168

DOI: 10.1016/0378-4371(93)90222-P

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