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arXiv · 1209.0951

The critical temperature for the Ising model on planar doubly periodic graphs

David Cimasoni·Hugo Duminil-Copin
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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 βfor a graph G with coupling constants (J_e)_{e\in E(G)} is obtained as the unique solution of a linear equation in the variables (\tanh(βJ_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. 2012-09-05. The critical temperature for the Ising model on planar doubly periodic graphs. https://arxiv.org/abs/1209.0951

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