Kramers-Wannier Approximation for the 3D Ising Model.

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  • Okunishi Kouichi
    Department of Applied Physics, Graduate School of Engineering, Osaka University, Suita 565–0871, Japan
  • Nishino Tomotoshi
    Department of Physics, Graduate School of Science, Kobe University, Kobe 657–8501, Japan

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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, Kc = 0.2184 , is only 1.5 % less than the true Kc. This result is better than that obtained using the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-field like.

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