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

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

2007-04-16

arxiv.org/abs/0704.1949v1

J. Phys. Soc. Jpn. 76 (2007) 084004

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1143/JPSJ.76.084004

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.

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