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• W2078168527 abstract "We establish an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d-regular tree, the so-called replica symmetric solution. For uniformly random d-regular graphs we further show that the replica symmetric Bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions." @default.
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• W2078168527 date "2014-03-13" @default.
• W2078168527 modified "2023-09-24" @default.
• W2078168527 title "The Replica Symmetric Solution for Potts Models on d-Regular Graphs" @default.
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• W2078168527 doi "https://doi.org/10.1007/s00220-014-1956-6" @default.
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