Growth model with restricted surface relaxation

TL;DR

This paper introduces a growth model with restricted surface relaxation, revealing a crossover from linear to nonlinear behavior in surface roughness evolution in one and two dimensions, depending on a parameter s.

Contribution

The study proposes a novel growth model with limited relaxation range and analyzes its crossover dynamics, extending understanding of surface growth processes.

Findings

In 1D, the growth exponent shows a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior.

In 2D, roughness exhibits logarithmic growth at short times and power-law at long times.

The crossover time depends on the relaxation distance parameter s.

Abstract

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson linear model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t_c which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times.