The critical temperature for the Ising model on planar doubly periodic graphs
The critical temperature for the Ising model on planar doubly periodic graphs
复制标题
平面双周期图伊辛模型的临界温度
DOI：
10.1214/ejp.v18-2352
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发表时间：
2012
影响因子：
1.4
通讯作者：
H. Duminil
中科院分区：
文献类型：
--
作者：
David Cimasoni;H. Duminil
本文给出了任意平面双周期加权图上伊辛模型的临界温度的一个简单刻画。更精确地说，具有耦合常数$（J_e）_{e\in E（G）}$的图$G$的临界逆温度$\beta$是以$（\tanh（\beta J_e））_{e\in E（G）}$为变量的代数方程的唯一解。这是通过使用Kac-Ward矩阵研究模型的高温膨胀来实现的。
We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature $\beta$ for a graph $G$ with coupling constants $(J_e)_{e\in E(G)}$ is obtained as the unique solution of an algebraic equation in the variables $(\tanh(\beta J_e))_{e\in E(G)}$. This is achieved by studying the high-temperature expansion of the model using Kac-Ward matrices.