Roughening of two-dimensional quasicrystal interfaces

The roughening of quasicrystal interfaces is studied in two dimensions via a simple lattice-gas model on a Penrose tiling. A detailed study of the mapping onto a one-dimensional quasiperiodic Schr\"odinger equation is carried out, a novel feature being the use of the dual method to calculate several parameters of the quantum model. Within the framework of this mapping, these parameters are shown to imply a nonzero roughening temperature. Although closer study shows that the mapping fails, it is argued that the conclusion that quasicrystals are less rough than crystals is unlikely to be affected.