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Arctic octahedron in threedimensional rhombus tilings and related integer solid partitions
 Journal of Statistical Physics
, 1989
"... Threedimensional integer partitions provide a convenient representation of codimensionone threedimensional 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 pr ..."
Abstract

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Threedimensional integer partitions provide a convenient representation of codimensionone threedimensional 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 fixedboundary tilings. Our results suggest that the ratio of free and fixedboundary entropies is sfree/sfixed=3/2, 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 threedimensional random tilings. KEY WORDS: Random tilings; integer partitions; configurational entropy; boundary effects; transition matrix Monte Carlo algorithms.