aqora

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)

Giichi Tanaka, Minoru Kimura

Progress of Theoretical PhysicsMay 1, 19940 citations

The cluster variation method and the method of the reducibility of density matrices

Shigetoshi Katsura, Ryoichi Kikuchi

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19843 citations

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

Matrix Form of Quantum Mechanics. Perturbation Theory. Density Matrix

WORLD SCIENTIFIC eBooksSep 27, 20160 citations

Structure of the Density Matrices in the Cluster Variation Method

Tomoyasu Tanaka, Kouzi Hirose, Kenpou Kurati

Two of the formulations of the cluster variation method are compared. The Heisenberg model of ferromagnetism in four-spin approximation is used as a working example. The numerical results obtained are used in the CAM analysis and an improved critical temperature is found. Formulations of the cluster variation method in the momentum space are also reviewed briefly.

Progress of Theoretical Physics SupplementJan 1, 19948 citations

A Variational Cluster Approximation for the Heisenberg Model

S Filor

In this thesis we present a novel variational cluster approximation for Heisenberg spin systems. It is based on the self-energy functional theory by Potthoff for fermionic and bosonic models with local interactions. To develop a similar method for spin systems, we derive a free energy functional which is the starting point of the approximation. Within this approximation, we find an analytical expression to evaluate the free energy by tiling the real system into a set of clusters. We describe the technical details of the spin variational cluster approximation and the evaluation of the free energy. The method is tested for the antiferromagnetic spin-1/2 Heisenberg chain with first- and second-neighbour interactions. Thereby, we investigate the dependence of the approximation on cluster size and the choice of variational parameters. The opportunities and limitations as well as future applications of the method are thoroughly discussed.In this thesis we present a novel variational cluster approximation for Heisenberg spin systems. It is based on the self-energy functional theory by Potthoff for fermionic and bosonic models with local interactions. To develop a similar method for spin systems, we derive a free energy functional which is the starting point of the approximation. Within this approximation, we find an analytical expression to evaluate the free energy by tiling the real system into a set of clusters. We describe the technical details of the spin variational cluster approximation and the evaluation of the free energy. The method is tested for the antiferromagnetic spin-1/2 Heisenberg chain with first- and second-neighbour interactions. Thereby, we investigate the dependence of the approximation on cluster size and the choice of variational parameters. The opportunities and limitations as well as future applications of the method are thoroughly discussed.

Jan 1, 20170 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)

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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)

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