Random deposition model with surface relaxation in higher dimensions

Wooseop Kwak and Jin Min Kim

Physica A: Statistical Mechanics and its Applications, 2019, vol. 520, issue C, 87-92

Abstract: A random deposition model with surface relaxation, so-called the Family model is studied in higher dimensions. In three dimensions, the surface width W(t) characterizing the roughness of a surface grows as 2blogt at the beginning and becomes saturated at 2alogL for t≫Lz, where L is the system size. The dynamic exponent z=1.99(2) is estimated from the relation z=a∕b and a nice data collapse of the scaling plot W2(L,t)∼logL2agt∕Lz is given with z=2. In four dimensions, the surface width approaches an intrinsic width Wint with a small correction term W2(L,t)=Wint2−L2αft∕Lz, where z≈1.97 and negative exponent α≈−0.52 are obtained. Our results support that the Family model belongs to the Edwards–Wilkinson universality class even in higher dimensions.

Keywords: Surface roughness; Family model; Negative exponent; Edwards–Wilkinson equation (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:520:y:2019:i:c:p:87-92

DOI: 10.1016/j.physa.2019.01.016

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