Universality and crossover behavior of single-step growth models in $1+1$ and $2+1$ dimensions

TL;DR

This study investigates the kinetic roughening of the single-step growth model in 1+1 and 2+1 dimensions, revealing a slow crossover from Edwards-Wilkinson to KPZ universality class for p<1/2, with detailed parameter analysis.

Contribution

The paper provides the first comprehensive numerical evidence that the single-step model with p≠1/2 belongs to the KPZ universality class in 2+1 dimensions, detailing crossover dynamics and parameters.

Findings

Existence of a slow crossover from EW to KPZ regime for p<1/2

Crossover time and KPZ parameters depend on p and decrease nonlinearly

Confirmation that the model belongs to KPZ universality class in 2+1 dimensions

Abstract

We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter $p$ in $1+1$ and $2+1$ dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an intermediate regime dominated by the Edwards-Wilkinson class to an asymptotic regime dominated by the Kardar-Parisi-Zhang (KPZ) class for any $p <\frac{1}{2}$. We also identify the crossover time, the nonlinear coupling constant, and some nonuniversal parameters in the KPZ equation as a function $p$. The effective nonuniversal parameters are continuously decreasing with $p$, but not in a linear fashion. Our results provide complete and conclusive evidence that the SS model for $p \neq \frac{1}{2}$ belongs to the KPZ universality class in $2+1$ dimensions.