The critical temperature for the Ising model on planar doubly periodic graphs
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 β for a graph G with coupling constants (Je)e∈ E(G) is obtained as the unique solution of a linear equation in the variables ((β Je))e∈ E(G). This is achieved by studying the high-temperature expansion of the model using Kac-Ward matrices.
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