Torpid Mixing of Markov Chains for the Six-vertex Model on ${\mathbb{Z}}^2$

Abstract

In this paper, we study the mixing time of two widely used Markov chain algorithms for the six-vertex model, Glauber dynamics and the directed-loop algorithm, on the square lattice ${\mathbb{Z}}^2$. We prove, for the first time that, on finite regions of the square lattice these Markov chains are torpidly mixing under parameter settings in the ferroelectric phase and the anti-ferroelectric phase.

Appeared in RANDOM 2018

References in corpus (1)

• The density profile of the six vertex model with domain wall boundary conditions