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arXiv · cond-mat/9712267

Random Tilings: Concepts and Examples

Christoph Richard·Moritz Hoeffe·Joachim Hermisson·Michael Baake
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Abstract

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.

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Christoph Richard, Moritz Hoeffe, Joachim Hermisson, Michael Baake. 1998-08-21. Random Tilings: Concepts and Examples. https://doi.org/10.1088/0305-4470%2F31%2F30%2F007

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