Anomalous Roughness in Dimer-Type Surface Growth

TL;DR

This paper investigates how geometric features influence surface growth dynamics, revealing anomalous scaling behavior in a dimer-based model due to topological constraints, with implications for non-equilibrium surface phenomena.

Contribution

It introduces a novel dimer deposition-evaporation model demonstrating anomalous roughness scaling caused by topological constraints.

Findings

Surface width scales as L^{1/3}, diverging with system size.

Pinning valleys and facets develop spontaneously.

Anomalous scaling arises from non-local evenness constraints.

Abstract

We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning valleys (hill tops) develop spontaneously and the surface facets for all growth (evaporation) biases. More intriguingly, the scaling properties of the rough one dimensional equilibrium surface are anomalous. Its width, $W\sim L^\alpha$, diverges with system size $L$, as $\alpha={1/3}$ instead of the conventional universal value $\alpha={1/2}$. This originates from a topological non-local evenness constraint on the surface configurations.