Thermodynamic behavior of a Penrose-tiling quasicrystal

Publisher Website
Google Scholar
Abstract
The Penrose tiling provides a prototype for the quasiperiodic crystal model of quasicrystals. We report results of Monte Carlo simulations of a two-dimensional model in which a Penrose tiling is the ground state. A single energy is assigned to any violation of the Penrose matching rules. Our results support the existence of two separate phase transitions, corresponding to single- and double-arrow matching-rule disorder, respectively. Manifestations of these transitions in the behavior of ‘‘perpendicular-space’’ quantities are explored. A limited exploration of the effects of unequal double- and single-arrow matching-rule-violation energies is performed. Speculations that the Penrose pattern might be inherently prone to glassy behavior are shown to be incorrect.

This publication has 8 references indexed in Scilit: