Mean-field approximations for the restricted solid-on-solid growth models

TL;DR

This paper investigates surface growth models with wetting and roughening transitions using mean-field approximations, providing analytical and numerical insights into phase behavior and interface dynamics.

Contribution

It introduces simple and pair mean-field approaches to analyze growth models, with the pair mean-field offering improved accuracy and exact solutions under detailed balance.

Findings

Simple mean-field predicts roughening transition and growth exponents.

Pair mean-field aligns better with simulations and captures interface velocity.

Under detailed balance, pair mean-field provides exact solutions.

Abstract

We study models for surface growth with a wetting and a roughening transition using simple and pair mean-field approximations. The simple mean-field equations are solved exactly and they predict the roughening transition and the correct growth exponents in a region of the phase diagram. The pair mean-field equations, which are solved numerically, show a better accordance with numerical simulation and correctly predicts a growing interface with constant velocity at the moving phase. Also, when detailed balance is fulfilled, the pair mean field becomes the exact solution of the model.