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 σσ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉〈w2〉 for two models in the 2+12+1-dimensional Kardar–Parisi–Zhang (KPZ) class and for a model in the 1+11+1-dimensional Villain–Lai–Das Sarma (VLDS) class. The values obtained from σσ provide consistent asymptotic estimates, eventually with smaller finite-size corrections. For the VLDS (nonlinear molecular beam epitaxy) class, we obtain α=0.93±0.01α=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 in terms of its universality class raised by numerical results and a recent derivation of its continuous equation. Effective exponents calculated from σσ suggest that both versions are in the KPZ class. Additional support for this conclusion is obtained by a comparison of the full-roughness distributions of these models and the distribution of other discrete KPZ models.