Exponential convergence to equilibrium for the d-dimensional East model

Abstract

Kinetically constrained models (KCMs) are interacting particle systems on $Z^d$ with a continuous-time constrained Glauber dynamics, which were introduced by physicists to model the liquid-glass transition. One of the most well-known KCMs is the one-dimensional East model. Its generalization to higher dimension, the d-dimensional East model, is much less understood. Prior to this paper, convergence to equilibrium in the d-dimensional East model was proven to be at least stretched exponential, by Chleboun, Faggionato and Martinelli in 2015. We show that the d-dimensional East model exhibits exponential convergence to equilibrium in all settings for which convergence is possible.

arXiv comment10 pages, 1 figure

References in corpus (5)

• Glassy dynamics of kinetically constrained models
• Non-equilibrium dynamics of spin facilitated glass models
• Relaxation times of kinetically constrained spin models with glassy dynamics
• Relaxation to equilibrium of generalized East processes on ${\mathbb{Z}}^d$: Renormalization group analysis and energy-entropy competition
• Mixing time and local exponential ergodicity of the East-like process in ${\mathbf{Z}}^d$

Cited by in corpus (3)

• On a front evolution problem for the multidimensional East model
• Kinetically constrained models out of equilibrium
• Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature