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

TL;DR

This paper introduces a method to estimate roughness exponents using fluctuations, demonstrating improved accuracy and clarifying the universality class of ballistic deposition models through numerical analysis and distribution comparisons.

Contribution

The paper proposes calculating effective roughness exponents from fluctuations, providing more accurate estimates and clarifying the universality class of ballistic deposition models.

Findings

Effective exponents from fluctuations yield consistent asymptotic estimates.

The VLDS class exponent is refined to alpha=0.93+-0.01.

Ballistic deposition models are confirmed to belong to the KPZ class.

Abstract

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.