Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method

Abstract

Two-dimensional ferromagnetic N-state clock models are studied on a hyperbolic lattice represented by tessellation of pentagons. The lattice lies on the hyperbolic plane with a constant negative scalar curvature. We observe the spontaneous magnetization, the internal energy, and the specific heat at the center of sufficiently large systems, where the fixed boundary conditions are imposed, for the cases N>=3 up to N=30. The model with N=3, which is equivalent to the 3-state Potts model on the hyperbolic lattice, exhibits the first order phase transition. A mean-field like phase transition of the second order is observed for the cases N>=4. When N>=5 we observe the Schottky type specific heat below the transition temperature, where its peak hight at low temperatures scales as N^{-2}. From these facts we conclude that the phase transition of classical XY-model deep inside the hyperbolic lattices is not of the Berezinskii-Kosterlitz-Thouless type.

REVTeX style, 4 pages, 6 figures, submitted to Phys. Rev. E

References in corpus (9)

• The density-matrix renormalization group
• Corner Transfer Matrix Renormalization Group Method
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Numerical Renormalization Group at Criticality
• Periodic boundary conditions on the pseudosphere
• Geometric effects on critical behaviours of the Ising model
• Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Phase Transition of XY Model in Heptagonal Lattice

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