On the origins of scaling corrections in ballistic growth models

TL;DR

This paper investigates the scaling corrections in ballistic growth models, identifies their origin, and proposes a binning method to accurately determine KPZ universality class exponents and distributions in 2+1 dimensions.

Contribution

It introduces a method to correct scaling analysis for intrinsic width effects and a binning technique to accurately extract universal fluctuations in ballistic growth models.

Findings

Scaling exponents align with KPZ class after correction.

Binning method effectively suppresses scaling corrections.

Height distributions match KPZ universality in 2+1 dimensions.

Abstract

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtained scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in divide the surface in bins of size $\varepsilon$ and use only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class were found. The binning method allowed the accurate determination of the height distributions of the ballistic models in both growth and steady state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in $2+1$ dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.