Modified Family-Vicsek Scaling and Probability Distributions for Brownian Castle Interfaces

Abstract

The Brownian Castle is a new interface growth model that is a variation on the well-known ballistic deposition model that results in an entirely new universality class. We present numerical verification that the interface width for BC interfaces displays modified Family-Vicsek scaling properties up to finite size corrections. Specifically, we find a growth exponent of $\beta=0.470 \pm 0.012$ and a roughness exponent of $\alpha=1.01 \pm 0.018$. The scaling is modified at short times with a size scaling exponent that described the early time dependence of interface width on length. The probability distribution of heights for the BC interface shows significant deviations from simple Gaussian behavior and the probability distribution of height changes shows a Cauchy-Lorentz form consistent with expectations for a process involving relatively large jumps.