2002/01/31 by M. Widom, R. Mosseri, N. Destainville +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Conjecture #Entropy (arrow of time) #Integer (computer science) #Markov Chains and Monte Carlo Methods #Monte Carlo method #Octahedron #Quasicrystal Structures and Properties #Random matrix #Rhombus #cond-mat.stat-mech
paper · pdf · doi:10.1023/a:1020464224385
published as J. Stat. Phys. 109, 945 (2002)
arxiv created 2003/01/14 · arxiv updated 2015/06/24
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 σfree/σfixed=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.