statistical physics

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

arXiv:2607.13922

summary

The paper introduces the Brownian Castle interface growth model and uses numerical simulations to show that its interface width follows a modified Family‑Vicsek scaling with specific growth and roughness exponents, while the height statistics deviate from Gaussian behavior and follow a Cauchy‑Lorentz distribution.

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 $I^^{2} = 0.470 \pm 0.012$ and a roughness exponent of $I^\pm = 1.01 \pm 0.018$ . 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.

Topics & keywords

#interface growth #scaling laws #universality class #non-gaussian statistics #probability distributionsFamily-Vicsek scalinggrowth exponent βroughness exponent αCauchy-Lorentz distributionballistic depositionnumerical simulation