Height Difference Correlation Function Research Articles

Ideal quasicrystal facets: A Monte Carlo study.

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.

Magnetic Correlation Function of the Two-Dimensional Planar Spin Model: Self-Consistent Calculation

with the exponent j)c~l. The susceptibility x is pro­ portional to ~}['cTJ, where the exponent r; takes the value 1/4 at 7',. The value r;(T,) =1'4 agrees with that by Kosterlitz or the experimental results, although the value v = l is different from v = 1/2 obtained by Kosterlitz. Step free energy and the height difference correlation function in the mDG model are also calculated.