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

L. Šamaj, Miroslav Kolesik

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)157-168
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Volume193
Issue number1
DOIs
StatePublished - Feb 15 1993
Externally publishedYes

Fingerprint

Self-duality
Vertex Model
Gauge Transformation
series expansion
apexes
Series Expansion
coordination number
free energy
Free Energy
Lowest
Gauge
Phase Transition
Higher Order
First-order
Internal
approximation
Arbitrary
Term
Approximation

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Self-duality of the O(2) gauge transformation and the phase structure of vertex models. / Šamaj, L.; Kolesik, Miroslav.

In: Physica A: Statistical Mechanics and its Applications, Vol. 193, No. 1, 15.02.1993, p. 157-168.

Research output: Contribution to journalArticle

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