Coherent-Anomaly Method in Two-Dimensional Antiferromagnetic Ising Models on Square and Triangular Lattices

Abstract

In the present paper we have applied the Coherent-Anomaly Method (CAM) [1] proposed by one of the authors (M.S.), to two-dimensional antiferromagnetic Ising models on square and triangular lattices. We determined both critical temperature T _c, and critical exponent γ as functions of a uniform external magnetic field H ranging from 0 to H _c. Estimations of T _c and γ were based on the results obtained within the Double-Cluster Approximation (DCA). In that approximation effective fields are obtained from selfconsistency conditions imposed on correlation functions of two different clusters. We have chosen pairs of wider and wider infinite stripes, which seems to be a very appropriate choice for two-dimensional models. A partition function of a stripe can be found as the largest eigen-value of the corresponding transfer matrix. This version of the CAM has been already applied to ferromagnetic Ising models as well as to Blume-Emery-Griffiths model, and is more thoroughly described in [2,3]. Our results can be summarized as follows.