Torpid Mixing of Markov Chains for the Six-vertex Model on ℤ²

2018/09/07 by Liu, Tianyu
#Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1809.02703

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 ℤ². 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.

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