J. Phys. Soc. Jpn. 76, 084004 (2007) [4 Pages]

Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane

+ Affiliations
1Department of Physics, Graduate School of Science, Kobe University, Kobe 657-85012Institute of Electrical Engineering, Slovak Academy of Sciences, SK-841 04 Bratislava, Slovakia

Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the lattice makes it possible to apply the corner transfer matrix renormalization group method. From the calculated nearest neighbor spin correlation function and the spontaneous magnetization, it is concluded that the phase transition of this model is mean-field like. One parameter deformation of the corner Hamiltonian on the hyperbolic plane is discussed.

©2007 The Physical Society of Japan