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

F.D.A. Aarão Reis

Physica A: Statistical Mechanics and its Applications, 2006, vol. 364, issue C, 190-196

Abstract: In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 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 σ provide consistent asymptotic estimates, eventually with smaller finite-size corrections. For the VLDS (nonlinear molecular beam epitaxy) class, we obtain α=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 σ 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.

Keywords: Growth models; Roughness exponent; Roughness distribution; Ballistic deposition; Kardar–Parisi–Zhang equation (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:364:y:2006:i:c:p:190-196

DOI: 10.1016/j.physa.2005.09.052

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