等径图上的统计力学
Statistical mechanics on isoradial graphs
摘要：
等径图是正则图的自然推广，它为统计力学的许多模型提供了研究临界模型的正确框架。在这篇综述论文中，我们首先解释了物理学家使用的两种方法：转移矩阵和共形域论中等径图是如何自然产生的。这导致我们的事实，即等径图提供了一个自然的设置离散复分析，我们专门一节。然后，我们给出了一个概述的明确的结果，为不同的模型定义的统计力学在这样的图形：临界二聚体模型时，底层图形是二分的，2维临界伊辛模型，随机游动和生成树和q-状态Potts模型。
英文摘要：
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natural setting for discrete complex analysis, to which we dedicate one section. Then, we give an overview of explicit results obtained for different models of statistical mechanics defined on such graphs: the critical dimer model when the underlying graph is bipartite, the 2-dimensional critical Ising model, random walk and spanning trees and the q-state Potts model.
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