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 I sing model, which contains two variational parameters. We numerically calcu late the variational partition function using the corner transfer matrix re normalization group (CTMRG) method, and find its maximum with respect to th e 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-held like.