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.
CTMRG as a tensor-network message-passing algorithm
National Science Center "Kharkiv Institute of Physics and Technology"（哈尔科夫物理与技术国家科学中心）；Haiqu, Inc.（海奎公司）；V.N. Karazin Kharkiv National University（V.N.卡拉金哈尔科夫国立大学）
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Center for Quantum Information, Communication and Computation (CQuICC)（量子信息、通信与计算中心）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models
Boston College（波士顿学院）；Washington University（华盛顿大学）；University of Oxford（牛津大学）；Technische Universität Chemnitz（开姆尼茨工业大学）；Indian Institute of Technology Madras（印度马德拉斯理工学院）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；Indiana University（印第安纳大学）
