Faceting and roughening in quasicrystals

Abstract

The question whether quasicrystal shapes should be faceted is studied in a simple model of quasicrystalline order. At T=0, the model is proved to yield a completely faceted equilibrium shape in both two and three dimensions. At T>0, an interface model is derived for a two-dimensional Penrose tiling. By mapping it onto a one-dimensional quasiperiodic Schrödinger equation, we show that the roughness exponent varies continuously with T at low T.