Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
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 pr...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Text |
| Language: | English |
| Published: |
1989
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| Subjects: | |
| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.545.9799 http://euler.phys.cmu.edu/widom/pubs/PDF/jsp109_2002_p945.pdf |
| Summary: | 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 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 three-dimensional random tilings. KEY WORDS: Random tilings; integer partitions; configurational entropy; boundary effects; transition matrix Monte Carlo algorithms. |
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