Study of Coherent Anomalies and Critical Exponents Based on High-Level Cluster-Variation Approximations

Abstract

The coherent-anomaly scaling property of the susceptibility for the Ising model is investigated using the Tanoji (a Chinese character which means a rice field) and cube cluster-approximations in the cluster-variation method on the square and simple cubic lattices, respectively. Estimates of the critical temperature and critical exponent are improved considerably by the inclusion of these high-level cluster-variation approximations in the coherent-anomaly extrapolation. It is also found that the dimensionality of the basic cluster is sensitive to the evaluation of critical exponents in higher dimensions.