New variational series expansions for lattice models

(Received 22 June 1992, accepted in final form 27 August 1992)

Abstract
For the symmetric two-state vertex model on the honeycomb lattice we construct a series expansion of the free energy which, at finite order, depends on free gauge parameters. We treat these gauge parameters as variational ones, and derive a canonical series of classical approximations which possesses the property of coherent anomaly. As a test model we use the vertex formulation of the Ising antiferromagnet in a field and, within the coherent-anomaly method, determine with a high accuracy its critical frontier and exponent . Numerical checks on the constancy of critical exponents along the phase boundary are presented, too.