The ising antiferromagnet and max cut on random regular graphs

Coja-Oghlan, Amin, Loick, Philipp, Mezei, Balazs F. and Sorkin, Gregory B. ORCID: 0000-0003-4935-7820 (2022) The ising antiferromagnet and max cut on random regular graphs. SIAM Journal on Discrete Mathematics, 36 (2). 1306 - 1342. ISSN 0895-4801

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Abstract

The Ising antiferromagnet is an important statistical physics model with close connections to the Max Cut problem. Combining spatial mixing arguments with the method of moments and the interpolation method, we pinpoint the replica symmetry breaking phase transition predicted by physicists. Additionally, we rigorously establish upper bounds on the Max Cut of random regular graphs predicted by Zdeborová and Boettcher [J. Stat. Mech., 2010 (2010), P02020]. As an application we prove that the information-theoretic threshold of the disassortative stochastic block model on random regular graphs coincides with the Kesten-Stigum bound.

Item Type:	Article
Official URL:	https://epubs.siam.org/journal/sjdmec
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	20 Jan 2022 10:45
Last Modified:	11 Feb 2025 17:21
URI:	http://eprints.lse.ac.uk/id/eprint/113471

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