Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
Statistical Mechanics
2015-06-24 v2
Abstract
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is , and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in three-dimensional random tilings.
Cite
@article{arxiv.cond-mat/0201309,
title = {Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions},
author = {M. Widom and R. Mosseri and N. Destainville and F. Bailly},
journal= {arXiv preprint arXiv:cond-mat/0201309},
year = {2015}
}