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摘要翻译：
证明了层次格上Potts模型重整化群的生成元可以用作用于复射影空间有限维积的有理映射来表示。在这个框架中，我们也可以考虑外加磁场和多自旋相互作用的模型。利用最近关于有理映射在多复变中迭代的结果，证明了对于一类层次格，Lee-Yang零点和Fisher零点属于重整化映射的不稳定集。
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英文标题：
《Potts models on hierarchical lattices and Renormalization Group dynamics》
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作者：
Jacopo De Simoi, Stefano Marmi
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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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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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英文摘要：
We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also consider models with an applied external magnetic field and multiple-spin interactions. We use recent results regarding iteration of rational maps in several complex variables to show that, for some class of hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of the renormalization map.
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PDF链接：
https://arxiv.org/pdf/708.0616
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