Boundary conditions, entropy and the signature of random tilings

Abstract

We investigate the influence of boundary conditions on the results of Monte Carlo simulations of 2D random tilings. Looking at the fluctuations in internal space we compare fixed and periodic boundaries. We find that fixed boundary conditions will lead to a different random tiling ensemble with reduced finite-size entropy density in comparison with periodic boundary conditions. As a by-product, we derive improved estimates for the elastic constants of the octagonal rhombus-tiling ensemble. Finally, we introduce a robust tool, also suitable for the analysis of experimental data, to distinguish between quasiperiodic and random-tiling models.