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Spin- Ising model by the cluster variation method and the path probability method

Osman Canko, Mustafa Keskín

Physica A Statistical Mechanics and its ApplicationsSep 7, 200514 citations

On the CAM Canonicality of the Cluster-Variation Approximations

Makoto Katori, Masuo Suzuki

The cluster-variation method (CVM) proposed by Kikuchi is a general theory to give approximations, which are useful to discuss phase transitions qualitatively in many systems. Recently one of the present authors (M. S.) proposed the coherent-anomaly method (CAM). If we have a well-behaved series of approximations, which is called a canonical series, we can estimate critical exponents following the CAM. In this paper it is demonstrated by using the ferromagnetic Ising models that the CVM will provide a canonical series which shows coherent anomaly. Our result implies that combining the CVM with the CAM will give a powerful method to study phase transitions and critical phenomena.The cluster-variation method (CVM) proposed by Kikuchi is a general theory to give approximations, which are useful to discuss phase transitions qualitatively in many systems. Recently one of the present authors (M. S.) proposed the coherent-anomaly method (CAM). If we have a well-behaved series of approximations, which is called a canonical series, we can estimate critical exponents following the CAM. In this paper it is demonstrated by using the ferromagnetic Ising models that the CVM will provide a canonical series which shows coherent anomaly. Our result implies that combining the CVM with the CAM will give a powerful method to study phase transitions and critical phenomena.

Progress of Theoretical Physics SupplementJan 1, 199410 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.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

Cluster Variation Method, Effective Field Method, and the Method of Integral Equation on the Regular and Random Ising Models

Shigetoshi Katsura

Springer eBooksJan 1, 19962 citations

Cluster variational theory of spin Ising models

J.W. Tucker

Journal of Magnetism and Magnetic MaterialsMay 1, 200032 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.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

Critical Phenomena of the S=1/2 Heisenberg-Ising Model Studied by CVM and CAM (Foundations and Applications of Cluster Variation Method and Path Probability Method) -- (Applications of Cluster Variation Method)

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Critical Phenomena of the S=1/2 Heisenberg-Ising Model Studied by CVM and CAM (Foundations and Applications of Cluster Variation Method and Path Probability Method) -- (Applications of Cluster Variation Method)

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