Kramers-Wannier Approximation for the 3D Ising Model | Zendy

Kouichi Okunishi | Zendy; Tomotoshi Nishino | Zendy

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Kramers-Wannier Approximation for the 3D Ising Model

Author(s) -

Kouichi Okunishi,

Tomotoshi Nishino

Publication year - 2000

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.103.541

Subject(s) - ising model , physics , renormalization group , square lattice ising model , transfer matrix , renormalization , partition function (quantum field theory) , mathematical physics , density matrix renormalization group , variational method , quantum mechanics , computer science , computer vision

We investigate the Kramers-Wannier approximation for the three-dimensional(3D) Ising model. The variational state is represented by an effective 2D Isingmodel, which contains two variational parameters. We numerically calculate thevariational partition function using the corner transfer matrix renormalizationgroup (CTMRG) method, and find its maximum with respect to the variationalparameters. The calculated transition point $K_{\rm c} = 0.2184$ is only 1.5%less than the true $K_{\rm c}$; the result is better than that obtained by thecorner transfer tensor renormalization group (CTTRG) approach. The calculatedphase transition is mean-field like.Comment: 7 pages, 4 figures, submitted to Prog. Theor. Phy

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