张量的高精度热力学和临界性质 重整化群流

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摘要翻译：
最近发展起来的张量重整化群(TRG)方法为导出晶格哈密顿量的热力学性质和临界性质提供了一种高精度的技术。TRG是一种局部粗粒化变换，每个晶格位的张量元素扮演了经历重整化群流的相互作用的部分。这些张量流与无限大系统的相图结构直接相关，每个相流都流向一个不同的不动点表面。沿流动的定点分析和求和给出了临界指数，以及沿整个温度范围的热力学函数。因此，对于铁磁三角晶格Ising模型，在整个温度范围内，自由能均优于10^-5。与以往的位置空间重整化群方法不同，该方法的截断（张量指数范围D）在简单和系统的改进下收敛。当D=24时，对应于4624维重整化群流，我们的最佳结果很容易得到。
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英文标题：
《High-Precision Thermodynamic and Critical Properties from Tensor
  Renormalization-Group Flows》
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作者：
Michael Hinczewski, A. Nihat Berker
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最新提交年份：
2007
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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：
  The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.
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PDF链接：
https://arxiv.org/pdf/709.2803

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关键词：高精度 热力学 interactions Improvements Hamiltonians TRG renormalization lattice 结果 系统