Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2

Author Tianyu Liu

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Author Details

Tianyu Liu
  • University of Wisconsin-Madison, Madison, WI, USA

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Tianyu Liu. Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Random walks and Markov chains
  • the six-vertex model
  • Eulerian orientations
  • square lattice
  • torpid mixing


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