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WORLD SCIENTIFIC eBooks

Coherent anomaly method : mean field, fluctuations and systematics

Masuo Suzuki

Published Jan 1, 1995• 10 citations
OpenAlex

Abstract

Overview cluster-variation power-series layered lattices spin glasses quantum percolation, random walk, SAW, DLA... stochastic processes.

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Coherent Anomaly Method Calculationon the Cluster Variation Method. II.Critical Exponents of Bond Percolation Model

Koh Wada, Naotosi Watanabe, Tetsuya Uchida

The critical exponents of the bond percolation model are calculated in the D (=2, 3,···)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s -state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s →1 limit of the s -state Potts model.

Journal of the Physical Society of Japan•Oct 15, 1991•5 citations

Structure of the Density Matrices in the Cluster Variation Method--Choices between Local Fields and Correlation Functions (Foundations and Applications of Cluster Variation Method and Path Probability Method) -- (Foundations of Cluster Variation Method)

Tomoyasu Tanaka, Kouzi Hirose, Kenpou Kurati

Progress of Theoretical Physics•May 1, 1994•0 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 Japan•Sep 1, 1987•73 citations
The critical exponents of the bond percolation model are calculated in the D (=2, 3,···)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s -state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s →1 limit of the s -state Potts model.
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.