Random walk diffusion model for a restricted solid-on-solid condition

Abstract

We study a random-walk diffusion model for a restricted solid-on-solid (RSOS) condition, where a deposited particle is allowed to walk randomly until visiting a site satisfying the RSOS condition. The interface width W grows as t β in early time, with β = 0.317 ± 0.005 in d = 1 + 1 dimension (β = 0.178±0.009 in d = 2+1 dimensions) and saturates at L α with α = 0.913±0.009 in d = 1+1 dimension (α = 0.638±0.008 in d = 2+1 dimensions). α and β satisfy a scaling relation α/β +α = 4 and are in good agreement with the values predicted by the conserved Langevin equation.