Roughness fluctuations, roughness exponents and the universality class   of ballistic deposition
  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. 
Fabio D. A. Aarao Reis