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Torpid Mixing of Markov Chains for the Six-vertex Model on $\mathbb{Z}^2$ (1809.02703v1)
Published 7 Sep 2018 in cs.DS and cs.DM
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.