Journal of the Physical Society of Japan

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

Sumiyoshi Fujiki, Makoto Katori, Masuo Suzuki

Published Aug 15, 1990• 18 citations

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.

DOI: 10.1143/jpsj.59.2681

Related papers

Study of Coherent Anomalies and Critical Exponents Based on the Cluster-Variation Method

Makoto Katori, Masuo Suzuki

The coherent-anomaly scaling is investigated for the approximations derived on the basis of the cluster-variation method (CVM). All of the mean-field critical coefficients are calculated in the Weiss, the Bethe and the Kikuchi approximations for the three-dimensional Ising model on the simple cubic lattice. The dynamical coefficients of the relaxation time are also obtained in the corresponding approximations for the kinetic Ising model. The non-classical values of critical exponents as well as the true value of critical temperature are estimated by extrapolating these approximants by the coherent-anomaly method. The results suggest that the approximations by the CVM possess the property of coherent-anomaly scaling.

Journal of the Physical Society of JapanNov 15, 198826 citations

Coherent-Anomaly Method Calculation on the Cluster Variation Method. I

Koh Wada, Naotosi Watanabe

On the basis of the coherent-anomaly method (CAM) proposed by Suzuki, the static and dynamic critical exponents of the Ising model in the triangle and the square lattice are calculated using the cluster variation method (CVM) and the path probability method (PPM) devised by Kikuchi within analytical tractable approximations. The values of critical temperatures and critical exponents estimated from three approximations with different levels are generally reasonable. The two-dimensional results are also compared with those of the simple cubic lattice.

Journal of the Physical Society of JapanDec 15, 198911 citations

Coherent Anomaly Method in Critical Phenomena. II. Applications to the Two- and Three-Dimensional Ising Models

Makoto Katori, Masuo Suzuki

A systematic procedure of constructing a series of cluster-mean-field approximations is established to investigate the coherent anomalies of the mean-field critical coefficients \barχ( L , T c ( L )) in the two- and three-dimensional Ising models. The values of critical exponents as well as the critical temperatures are estimated by means of the new method (Coherent Anomaly Method) as T c * =2.230(0.038) J / k B , γ=1.785(0.116) for the two-dimensional square lattice and T c * =4.529(0.058) J / k B , γ=1.258(0.068) for the three-dimensional simple cubic lattice. The results suggest that the present approach to study critical phenomena is very promising.

Journal of the Physical Society of JapanSep 1, 198773 citations

The CAM Calculation of Critical Exponent ν by the Cluster Variation Method

Koh Wada, Naotoshi Watanabe

The critical exponent ν of correlation length is calculated on the basis of the coherent anomaly method (CAM) by using the pair, the cactus-square and the square approximations of the cluster variation method (CVM) in the D (≥2)-dimensional cubic lattice of the Ising model. These simple analytical approximations give good values of critical exponent ν and critical temperature in the two- and three-dimensional lattices. However, further consideration is needed to determine a critical dimension in the D -dimensional Ising model by the CAM.

Journal of the Physical Society of JapanAug 15, 19909 citations

The Correlation Length and the Critical Exponentνthrough the Simplified Cluster Variation Method and the Coherent Anomaly Method

Je-Young Choi

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.

Journal of the Physical Society of JapanJan 15, 19973 citations

Accurate estimates of 3D Ising critical exponents using the Coherent-Anomaly Method

Miroslav Kolesik, Masuo Suzuki

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

Jan 1, 200812 citations