Abstract
We calculate the configurational entropy of codimension-one three-dimensional random rhombus tilings. We use three-dimensional integer partitions to represent these tilings. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We explore free- as well as fixed-boundary conditions and our numerical 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 ratio confirms a conjecture by Linde et al. concerning the ‘arctic octahedron phenomenon’ in three-dimensional codimension-one random tilings.
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