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

Abstract

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.

4 pages, 5 figures

References in corpus (5)

• The density-matrix renormalization group
• Geometric effects on critical behaviours of the Ising model
• Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
• Real-space renormalization group approach for the corner Hamiltonian
• Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

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