Comment on "Dynamic properties in a family of competitive growing models"

TL;DR

This paper critically examines previous claims about the scaling behavior of surface width in competitive growth models, demonstrating that those claims are incorrect through analysis and simulations.

Contribution

The authors refute prior assertions about power-law scaling and universal functions in competitive surface-growth models, providing corrected insights.

Findings

Previous power-law scaling claims are incorrect.

Universal scaling functions do not hold as previously claimed.

The actual behavior of surface width differs from earlier predictions.

Abstract

The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The claim is made that at saturation the surface width $w(p)$ obeys a power-law scaling $w(p) \propto 1/p^{\delta}$, where $\delta$ is only either $\delta =1/2$ or $\delta=1$, which is illustrated by the models where X is ballistic deposition and where X is RD with surface relaxation. Another claim is that in the limit $p \to 0^+$, for any lattice size $L$, the time evolution of $w(t)$ generally obeys the scaling $w(p,t) \propto (L^{\alpha}/p^{\delta}) F(p^{2\delta}t/L^z)$, where $F$ is Family-Vicsek universal scaling function. We show that these claims are incorrect.