research-article

The Ising Antiferromagnet and Max Cut on Random Regular Graphs

Authors:

Amin Coja-Oghlan,

Philipp Loick, Balázs F. Mezei,

Gregory B. SorkinAuthors Info & Claims

SIAM Journal on Discrete Mathematics, Volume 36, Issue 2

Pages 1306 - 1342

https://doi.org/10.1137/20M137999X

Published: 01 January 2022 Publication History

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.

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Cited By

Caramanis CFotakis DKalavasis AKontonis VTzamos COh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Optimizing solution-samplers for combinatorial problemsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3666741(14035-14069)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3666741

Index Terms

The Ising Antiferromagnet and Max Cut on Random Regular Graphs
1. Mathematics of computing
2. Theory of computation

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics Volume 36, Issue 2

Jun 2022

612 pages

ISSN:0895-4801

DOI:10.1137/sjdmec.36.2

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© 2022, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2022

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Cited By

Caramanis CFotakis DKalavasis AKontonis VTzamos COh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Optimizing solution-samplers for combinatorial problemsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3666741(14035-14069)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3666741

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