Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

TL;DR

This study investigates a 1+1D growth model combining ballistic and random deposition, revealing a slow crossover from Edwards-Wilkinson to KPZ universality class, with scaling relations connecting the crossover parameter p to KPZ nonlinear coefficient lambda.

Contribution

It demonstrates how the crossover from EW to KPZ universality occurs in a mixed deposition model and quantifies the relation between p and lambda, including the crossover time scaling.

Findings

The system exhibits KPZ scaling for any p>0.

The crossover time scales as p^(-8), confirming theoretical predictions.

Interface width and saturation time follow expected KPZ exponents with strong corrections.

Abstract

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient of the nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma = 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.