Random deposition model with surface relaxation in higher dimensions

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.