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Pré-Publication, Document De Travail Année : 2023

Kawasaki dynamics beyond the uniqueness threshold

Résumé

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random $d$-regular graph mixes fast beyond the tree uniqueness threshold when $d$ is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all $d\geq 3$). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial.
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Dates et versions

hal-04236370 , version 1 (10-10-2023)

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  • HAL Id : hal-04236370 , version 1

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Roland Bauerschmidt, Thierry Bodineau, Benoît Dagallier. Kawasaki dynamics beyond the uniqueness threshold. 2023. ⟨hal-04236370⟩
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