Flip dynamics in octagonal rhombus tiling sets

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving three tiles which sample the tiling sets via Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite tem...

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Bibliographic Details
Published in:Physical review letters 2002-01, Vol.88 (3), p.030601-030601, Article 030601
Main Author: Destainville, N
Format: Article
Language:English
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Summary:We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving three tiles which sample the tiling sets via Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size N(T) like const.xN(2)(T)lnN(T); these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.88.030601