## 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 language | English (US) |
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Pages (from-to) | 157-168 |

Number of pages | 12 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 193 |

Issue number | 1 |

DOIs | |

State | Published - Feb 15 1993 |

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics