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 Schrödinger 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.
ASJC Scopus subject areas
- Condensed Matter Physics