The Ising antiferromagnet in the replica symmetric phase

TL;DR

This paper analyzes the limiting distribution of the partition function for the Ising antiferromagnet on random regular graphs within the replica symmetric phase, using advanced probabilistic and combinatorial methods.

Contribution

It characterizes the distribution of the partition function in the replica symmetric phase up to the Kesten-Stigum bound, employing the method of moments and spatial mixing techniques.

Findings

Partition function distribution characterized up to Kesten-Stigum bound.

Method of moments and spatial mixing effectively analyze the model.

Provides insights into the phase transition behavior of the Ising model.

Abstract

Partition functions are an important research object in combinatorics and mathematical physics [Barvinok, 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.