Random tilings of high symmetry: I. Mean-field theory

Details Random tilings of high symmetry: I. Mean-field theory Random tilings of high symmetry: I. Mean-field theory

2003-10-22

arxiv.org/abs/cond-mat/0310514v2

J. Stat. Phys. 120, 799 (2005)

Physics

Condensed Matter

Statistical Mechanics

Published version. Some discussions have been simplified

Scientific paper

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.

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