Study on Phase Transitions of Antiferromagnetic Ising Models Using the Coherent-Anomaly Method

Abstract

The coherent-anomaly method proposed by one of the authors (M.S.) combined with a transfer-matrix version of the double-cluster approximation is applied to antiferromagnetic Ising models. We determined both the critical temperature and the critical exponent γ as functions of an external magnetic field. For a square lattice, our results are in a good agreement with the ones obtained recently by the phenomenological renormalization method. For triangle and simple cubic lattices, our results are less definite but still in a qualitative agreement with values predicted by other methods.