Transitions in a Probabilistic Interface Growth Model

TL;DR

This paper investigates a probabilistic interface growth model, revealing how different growth probabilities lead to various universality classes in one and two spatial dimensions through extensive simulations.

Contribution

It introduces a generalized growth rule with a tunable parameter, demonstrating how it causes crossovers between known universality classes in interface growth models.

Findings

In 1+1D, small $ u$ leads to Mullins-Herring to EW crossover.

Intermediate $ u$ causes EW to KPZ crossover.

Large $ u$ results in KPZ universality.

Abstract

We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding is strongest. We introduce a growth probability which is proportional to a power of the number $n_i$ of bindings of the site $i$: $p_i\propto n_i^\nu$. Through extensively simulations, in $(1+1)$-dimensions, we find three behavior depending of the $\nu$ value: {\it i}) if $\nu$ is small, a crossover from the Mullins-Hering to the Edwards-Wilkinson (EW) universality class; {\it ii}) for intermediate values of $\nu$, a crossover from the EW to the Kardar-Parisi-Zhang (KPZ) universality class; {\it iii}) and, finally, for large $\nu$ values, the system is always in the KPZ class. In $(2+1)$-dimensions, we obtain three different behaviors: {\it i}) a crossover from the Villain-Lai-Das Sarma to the EW universality class, for small $\nu$ values; {\it ii}) the EW class is always present, for intermediate $\nu$ values; {\it iii}) a deviation from the EW class is observed, for large $\nu$ values.