Random Tilings: Concepts and Examples

Details Random Tilings: Concepts and Examples Random Tilings: Concepts and Examples

1997-12-22

arxiv.org/abs/cond-mat/9712267v2

J. Phys. A: Math. Gen. 31 (1998) 6385-6408

Physics

Condensed Matter

Statistical Mechanics

32 pages, 42 eps-figures, Latex2e updated version, minor grammatical changes

Scientific paper

10.1088/0305-4470/31/30/007

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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