Kramers-Wannier Approximation for the 3D Ising Model

We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix re...

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Bibliographic Details
Published in:Progress of theoretical and experimental physics 2000-03, Vol.103 (3), p.541-548
Main Authors: Okunishi, Kouichi, Nishino, Tomotoshi
Format: Article
Language:English
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Summary:We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational parameters. The value of the calculated transition point, K c = 0.2184, is only 1.5% less than the true K c. This result is better than that obtained using the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-field like.
ISSN:0033-068X
2050-3911
1347-4081
DOI:10.1143/PTP.103.541