Abstract
Using the Sherman theorem on paths, the cluster property, and the second GKS inequality, we obtain some results in favor of the nonexistence of non-translation-invariant equilibrium states for twodimensional Ising models with ferromagnetic short-range interactions in the low-temperature region. With a constraint on the interaction strength at the boundary, we prove that for the two-dimensional Ising model, all boundary conditions yield the unique translation-invariant correlation functions 〈σX〉ℤ2,+, for |X| even.
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Supported by the Fonds National Suisse de la Recherche Scientifique.
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Merlini, D. Boundary conditions and cluster property in two-dimensional Ising ferromagnets. J Stat Phys 21, 739–745 (1979). https://doi.org/10.1007/BF01107912
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DOI: https://doi.org/10.1007/BF01107912