Learning universality and scaling from simple deposition models

TL;DR

This paper investigates how simple deposition models exhibit universal scaling behavior in surface growth, analyzing the impact of local relaxation parameters within the Edwards-Wilkinson class.

Contribution

It introduces the concepts of universality and scaling in deposition models and examines the nontrivial role of local relaxation distance within these models.

Findings

Deposition models belong to the Edwards-Wilkinson universality class.

The local relaxation parameter $\delta$ influences surface roughening behavior.

Scaling properties are qualitatively and quantitatively affected by relaxation processes.

Abstract

We use deposition models of kinetic roughening of a growing surface to introduce the concepts of universality and scaling and to analyze the qualitative and quantitative role of different parameters. In particular, we focus on two classes of models where the deposition is accompanied by a local relaxation process within a distance $\delta$. The models are in the Edwards-Wilkinson universality class, but the role of $\delta$ is nontrivial.