2022
DOI: 10.48550/arxiv.2203.07771
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Optimal mixing for two-state anti-ferromagnetic spin systems

Abstract: A. We prove an optimal Ω −1 lower bound for modified log-Sobolev (MLS) constant of the Glauber dynamics for anti-ferromagnetic two-spin systems with vertices in the tree uniqueness regime. Specifically, this optimal MLS bound holds for the following classes of two-spin systems in the tree uniqueness regime:• all strictly anti-ferromagnetic two-spin systems (where both edge parameters , < 1), which cover the hardcore models and the anti-ferromagnetic Ising models; • general anti-ferromagnetic two-spin systems o… Show more

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