On the origins of scaling corrections in ballistic growth models

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 $\epsilon$ 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.

arXiv comment8 pages, 7 figures

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• Kinetic interfaces of patchy particles
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• Effects of the growth kinetics on solute diffusion in porous films
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Transition from compact to porous films in deposition with temperature activated diffusion
• Height distributions in interface growth: The role of the averaging process