Transfer-matrix analysis of a two-dimensional quasicrystal

Abstract

We investigate the quasicrystalline state of a two-dimensional binary alloy in a discrete tiling approximation. Through transfer-matrix calculations we determine the configurational entropy over a range of concentrations. We find that the entropy density is maximized by a state with tenfold symmetry at the quasicrystal concentration. Derivatives of the entropy density at its maximum yield values for the phason elastic constants. Our results confirm the existence of quasi-long-range translational order in equilibrium quasicrystalline alloys and lend support to the random-tiling model of quasicrystals.