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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| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2002
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.cond-mat/0201309 https://arxiv.org/abs/cond-mat/0201309 |
| 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 $σ_{free}/σ_{fixed}=3/2$, 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. |
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