Numerical Examination of the Universality of the Equilibrium Crystal Shape in Some SOS Models

Abstract

By means of the Monte Carlo twist method, we examine the universality of the following critical properties of the equilibrium crystal shape in the discrete Gaussian (DG) model and restricted solid-on-solid (RSOS) model: c1) a finite curvature jump at the roughening temperature T R , c2) the profile of a facet with a singularlity at the facet edge for T < T R , and c3) the radius of the facet near T R proportional to \(\exp(-a/ \sqrt{1-T/T_{R}})\). We obtain the following results with the help of some results obtained analytically. The DG and RSOS models have T R =1.44 ±0.02 and 1.60 ±0.05, respectively. c2) is universal for these models. For the DG model c1) well agrees with the exact result of the body-centered SOS model, whereas for the RSOS model it is almost equal to twice the latter. Finite-size-scaling for c3) is excellent for the DG model, while it is consistent but inconclusive for the RSOS model.