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2013 The critical temperature for the Ising model on planar doubly periodic graphs
David Cimasoni, Hugo Duminil-Copin
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Electron. J. Probab. 18: 1-18 (2013). DOI: 10.1214/EJP.v18-2352

Abstract

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.

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David Cimasoni. Hugo Duminil-Copin. "The critical temperature for the Ising model on planar doubly periodic graphs." Electron. J. Probab. 18 1 - 18, 2013. https://doi.org/10.1214/EJP.v18-2352

Information

Accepted: 28 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1281.82004
MathSciNet: MR3040554
Digital Object Identifier: 10.1214/EJP.v18-2352

Subjects:
Primary: 82B20

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