Flip dynamics in octagonal rhombus tiling sets

Details Flip dynamics in octagonal rhombus tiling sets Flip dynamics in octagonal rhombus tiling sets

2001-01-26

arxiv.org/abs/cond-mat/0101413v3

Phys. Rev. Lett. 88 (3), 030601 (2002)

Physics

Condensed Matter

Statistical Mechanics

5 Revtex pages, 4 figures; definitive version

Scientific paper

10.1103/PhysRevLett.88.030601

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em 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 $Cst. N_T^2 \ln N_T$; 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.

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