Roughness fluctuations, roughness exponents and the universality class of ballistic deposition

Fabio D. A. Aarao Reis

Published 2005-10-03Version 1

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation (sigma) in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness <w_2> for two models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class and for a model in the 1+1-dimensional Villain-Lai-Das Sarma (VLDS) class. The values obtained from sigma provide consistent asymptotic estimates, eventually with smaller finite-size corrections. For the VLDS (nonlinear molecular beam epitaxy) class, we obtain alpha=0.93+-0.01, improving previous estimates. We also apply this method to two versions of the ballistic deposition model in two-dimensional substrates, in order to clarify the controversy on its universality class raised by numerical results and a recent derivation of its continuous equation. Effective exponents calculated from sigma suggest that both versions are in the KPZ class. Additional support to this conclusion is obtained by a comparison of the full roughness distributions of those models and the distribution of other discrete KPZ models.