2014/09/08 by Sidiney G. Alves, Tiago J. Oliveira, Silvio C. Ferreira · 1 citation
Mathematics · Physics and Astronomy · #Ansatz #Bin #Condensed matter physics #Exponent #Geometry #Mathematics #Physics #Quantum mechanics #Random Matrices and Applications #Renormalization group #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.052405
published as Phys. Rev. E 90, 052405 (2014) · 8 pages, 7 figures
arxiv created 2014/09/08 · openalex publication_date 2014/11/20 · arxiv updated 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 obtain scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in dividing the surface in bins of size ɛ and using only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class are found. The binning method allows 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.