License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.52
URN: urn:nbn:de:0030-drops-94568
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9456/
Liu, Tianyu
Torpid Mixing of Markov Chains for the Six-vertex Model on 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 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.
BibTeX - Entry
@InProceedings{liu:LIPIcs:2018:9456,
author = {Tianyu Liu},
title = {{Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
pages = {52:1--52:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-085-9},
ISSN = {1868-8969},
year = {2018},
volume = {116},
editor = {Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9456},
URN = {urn:nbn:de:0030-drops-94568},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2018.52},
annote = {Keywords: the six-vertex model, Eulerian orientations, square lattice, torpid mixing}
}
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Keywords: |
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the six-vertex model, Eulerian orientations, square lattice, torpid mixing |
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Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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13.08.2018 |
