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WORLD SCIENTIFIC eBooks

Coherent-Anomaly Analysis with Cluster Variation Method for Spin-Pair Correlation Function of Ising Model on Square Lattice

Kazuyuki Tanaka, Tsuyoshi Horiguchi, Tohru Morita

Published Sep 1, 1995• 0 citations
Publisher
DOI
10.1142/9789812797087_0020

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The spin-pair correlation functions in the Ising model with nearest-neighbor interaction J>0 and next-nearest-neighbor interaction J′ on the square lattice are obtained in three approximations of the simplified cluster variation method. We estimate the critical indices ην, γ and ν, by applying the coherent-anomaly method to the obtained spin-pair correlation functions. We conclude that the system belongs to the Onsager universality class when J′/J > −0.5 and does not when J′/J < −0.5.
The correlation length of the Ising model on the simple cubic lattice is calculated directly from the magnetization profiles which are determined in the pair, the square, and the cube approximations in the simplified cluster variation method. The critical exponent ν is obtained by applying the coherent anomaly method to the correlation length. The wave-number dependent magnetic susceptibility or the spin-pair correlation function is not required in obtaining the expression for the correlation length.