Ideal quasicrystal facets: A Monte Carlo study

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Abstract
The thermal behavior of optimal (faceted at T=0) interfaces in perfect quasiperiodic structures is investigated in two (2D) and three dimensions (3D) using Monte Carlo and renormalization-group techniques. Such interfaces in 2D are always rough, with a temperature-dependent roughness exponent less than the value of 1/2 for crystals. In 3D, we study the height-difference correlation function, surface energies, surface heat capacities, and step energies. We find that the interfaces get microscopically rougher with increasing temperature through a series of pseudoroughening transitions. However, the interfaces remain faceted and show no real roughening transition. Tilted interfaces, which are not optimal, are always found to be rough.