Random Tilings: Concepts and Examples
摘要
We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.
引用
@article{arxiv.cond-mat/9712267,
title = {Random Tilings: Concepts and Examples},
author = {Christoph Richard and Moritz Hoeffe and Joachim Hermisson and Michael Baake},
journal= {arXiv preprint arXiv:cond-mat/9712267},
year = {2008}
}
备注
32 pages, 42 eps-figures, Latex2e updated version, minor grammatical changes