Dynamic Scaling in a 2+1 Dimensional Limited Mobility Model of Epitaxial Growth

TL;DR

This paper investigates dynamic scaling and statistical invariance in a 2+1 dimensional limited mobility model of surface growth, revealing transient anomalous scaling behaviors similar to lower-dimensional cases through large-scale simulations.

Contribution

It introduces a simple 2+1D model for epitaxial growth and characterizes its scaling exponents, bridging discrete simulations with continuum theories.

Findings

Identification of long-lived transient anomalous scaling

Observation of multiaffine dynamic scaling properties

Quantitative comparison with continuum models

Abstract

We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening properties of molecular beam epitaxy. The model exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling properties similar to that found in the corresponding 1+1 - dimensional problem. Using large-scale simulations we obtain the relevant scaling exponents, and compare with continuum theories.