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

L. Šamaj, M. Kolesík

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)157-168
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - Feb 15 1993

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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