Random-tiling quasicrystal

Publisher Website
Google Scholar
Abstract
The quasicrystalline phase in the two-dimensional model explored by Widom, Strandburg, and Swendsen is shown by analysis of size dependence to be very well described by a random-tiling model in which a class of configurations corresponding to tilings of the plane with rhombuses are assumed to occur with equal weight. The existence of the quasicrystalline phase in this system is thus due to entropic effects. Despite the inherent phason disorder, the system is shown to possess quasi-long-range translational order. The phason elastic constant is obtained from the simulation and is temperature independent to within our statistical errors within the quasicrystalline phase. The value is in good agreement with transfer-matrix calculations for the appropriate random tilings and with Monte Carlo simulations for random tilings. The behavior of the system for temperatures above and below the random-tiling phase is briefly discussed.

This publication has 18 references indexed in Scilit: