摘要翻译：
在由五边形镶嵌表示的双曲晶格上研究了二维铁磁n态时钟模型。晶格位于具有常负标量曲率的双曲面上。对于n>=3到n=30的情况，我们观察了在足够大的系统中，施加固定边界条件时，中心的自发磁化强度、内能和比热。n=3的模型与双曲晶格上的三态Potts模型等价，表现出一级相变。在n>=4的情况下，观察到二级平均场相变。当n>=5时，我们观察到低于转变温度的肖特基型比热，其低温峰值为n^{-2}。根据这些事实，我们得出双曲晶格内部的经典XY模型的相变不是Berezinskii-Kosterlitz-Thouless型的。
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英文标题：
《Phase transition of clock models on hyperbolic lattice studied by corner
  transfer matrix renormalization group method》
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作者：
Andrej Gendiar, Roman Krcmar, Kouiji Ueda and Tomotoshi Nishino
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/801.0836