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

N. Destainville, M. Widom, R. Mosseri, F. Bailly

Published 2003-10-22, updated 2005-12-19Version 2

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.