The arctic octahedron phenomenon in three-dimensional codimension-one rhombohedral tilings
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چکیده
We calculate the configurational entropy of codimension-one three-dimensional random rhombus tilings. We use threedimensional integer partitions to represent these tilings. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We explore freeas well as fixed-boundary conditions and our numerical results suggest that the ratio of freeand fixed-boundary entropies is rfree=rfixed 1⁄4 3=2, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This ratio confirms a conjecture by Linde et al. concerning the arctic octahedron phenomenon’ in three-dimensional codimension-one random tilings. 2004 Elsevier B.V. All rights reserved. PACS: 05.10.Ln; 05.70.)a; 61.44.Br
منابع مشابه
Arctic Octahedron in Three-Dimensional Rhombus Tilings and Related Integer Solid Partitions
1 Carnegie Mellon University, Department of Physics, Pittsburgh, Pennsylvania 15213. 2 Groupe de Physique des Solides, Universités Paris 6 et 7, 2 place Jussieu, 75251 Paris Cedex 05, France. 3 Laboratoire de Physique Quantique, UMR CNRS-UPS 5626, Université Paul Sabatier, 31062 Toulouse Cedex 04, France; e-mail: [email protected] 4 Laboratoire de Physique du Solide-CNRS, ...
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تاریخ انتشار 2004