Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions

Abstract

We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves \textit{et al}. [Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account. In the present work, we show that this concept holds for $d=3+1$ and 4+1 dimensions. We have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models, presenting small finite-time corrections to the scaling, that in principle belong to the Kardar-Parisi-Zhang (KPZ) universality class in both $d=3+1$ and 4+1. Our results constitute a new evidence that the upper critical dimension of the KPZ class, if it exists, is larger than 4.

8 pages, 7 figures

References in corpus (9)

• Growing interfaces uncover universal fluctuations behind scale invariance
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
• Interface fluctuations for deposition on enlarging flat substrates
• On the origins of scaling corrections in ballistic growth models
• Growth exponents of the etching model in high dimensions
• Finite-size effects in roughness distribution scaling

Cited by in corpus (9)

• Universality of (2+1)-dimensional restricted solid-on-solid models
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• 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
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• Dimensional crossover in Kardar-Parisi-Zhang growth