Kawasaki dynamics beyond the uniqueness threshold

Abstract

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 $d\ge 3$). 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.

Improved presentation

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Cited by in corpus (2)

• Stochastic dynamics and the Polchinski equation: an introduction
• Fast and Slow Mixing of the Kawasaki Dynamics on Bounded-Degree Graphs