Dynamical surface structures in multi-particle-correlated surface growths

TL;DR

This paper studies the scaling and surface structures in multi-particle-correlated surface growth models with a conservation law, revealing universal roughness in equilibrium and diverse behaviors out of equilibrium.

Contribution

It introduces and analyzes $Q$-mer and $Q$-particle-correlated models, highlighting their universal and diverse surface roughness and structures under different conditions.

Findings

Equilibrium roughness is universal with exponent 1/3.

Early time growth exponent varies with model and Q.

Nonequilibrium surfaces exhibit faceted or grooved structures.

Abstract

We investigate the scaling properties of the interface fluctuation width for the $Q$-mer and $Q$-particle-correlated deposition-evaporation models. These models are constrained with a global conservation law that the particle number at each height is conserved modulo $Q$. In equilibrium, the stationary roughness is anomalous but universal with roughness exponent $\alpha=1/3$, while the early time evolution shows nonuniversal behavior with growth exponent $\beta$ varying with models and $Q$. Nonequilibrium surfaces display diverse growing/stationary behavior. The $Q$-mer model shows a faceted structure, while the $Q$-particle-correlated model a macroscopically grooved structure.