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)|
|Number of pages||12|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - Feb 15 1993|
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics