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

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  • Šamaj, L.
  • Kolesík, M.

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.

Suggested Citation

  • Šamaj, L. & Kolesík, M., 1993. "Self-duality of the O(2) gauge transformation and the phase structure of vertex models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 193(1), pages 157-168.
    • Handle: RePEc:eee:phsmap:v:193:y:1993:i:1:p:157-168
    DOI: 10.1016/0378-4371(93)90222-P
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    1. Šamaj, L. & Kolesík, M., 1992. "Mapping of the symmetric vertex model onto the Ising model for an arbitrary lattice coordination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(3), pages 455-466.
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