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Critical Temperature of Periodic Ising Models

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A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice L of Z^2. We give an exact, quantitative description of the critical temperature, defined by the supreme of the temperatures at which the spontaneous magnetization of a periodic, Ising ferromagnets is nonzero, as the solution of a certain algebraic equation, namely, the condition that the spectral curve of the corresponding dimer model on the Fisher graph has a real node on the unit torus.

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