The Ising antiferromagnet in the replica symmetric phase

Christian Fabian, Philipp Loick

Partition functions are an important research object in combinatorics and mathematical physics [Bavinok, 2016]. In this work, we consider the partition function of the Ising antiferromagnet on random regular graphs and characterize its limiting distribution in the replica symmetric phase up to the Kesten-Stigum bound. Our proof relies on a careful execution of the method of moments, spatial mixing arguments and small subgraph conditioning.

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