J. Phys. I France
Volume 3, Numéro 1, January 1993
Page(s) 93 - 106
DOI: 10.1051/jp1:1993119
J. Phys. I France 3 (1993) 93-106

New variational series expansions for lattice models

M. Kolesík and L. Samaj

Institute of Plysics, Slovak Academy of Sciences, Dúbravská cesta 9, 842 28 Bratislava, Czechoslovakia

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

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 $\gamma$. Numerical checks on the constancy of critical exponents along the phase boundary are presented, too.

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© Les Editions de Physique 1993

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