Universal and nonuniversal features in the crossover from linear to nonlinear interface growth

TL;DR

This paper investigates the crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang scaling in a 1D RSOS model, deriving the KPZ equation analytically, confirming a linear lambda-q relation, and estimating crossover times with high precision.

Contribution

It analytically derives the KPZ equation for the model, revealing a linear lambda-q relation, and provides precise numerical estimates of crossover times, contrasting with previous universal parabolic laws.

Findings

The KPZ nonlinear coefficient lambda is proportional to p-1/2.

The interface shows pure EW and KPZ scaling in specific p ranges.

Crossover times scale as t_c ~ lambda^(-4.1), matching theoretical predictions.

Abstract

We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p~0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q=p-1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear \lambda-q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55<=p<=0.8, which provides numerical estimates of the crossover times t_c. They scale as t_c ~ lambda^(-phi) with phi=4.1+-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi~3.