Parameter free scaling relation for nonequilibrium growth processes

TL;DR

This paper introduces a parameter-free scaling relation that achieves data collapse across various nonequilibrium growth models, offering a more universal approach than the traditional Family-Vicsek relation.

Contribution

The paper presents a novel, parameter-free scaling relation that applies broadly to nonequilibrium growth processes, improving upon existing models like Family-Vicsek.

Findings

The new scaling relation successfully collapses data for multiple growth models.

It outperforms the Family-Vicsek relation in certain regimes.

The relation is demonstrated on models including RD/RDSR and RSOS.

Abstract

We discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this new scaling relation through various growth models, as for example the competitive growth model RD/RDSR (random deposition/random deposition with surface diffusion) and the RSOS (restricted solid-on-solid) model with different nearest-neighbor height differences, as well as through a new deposition model with temperature dependent diffusion. The new scaling relation is compared to the familiar Family-Vicsek relation and the limitations of the latter are highlighted.