Universality and corrections to scaling in the ballistic deposition model

Abstract

In order to analyze some controversies on the equivalence between ballistic deposition (BD) and the Kardar-Parisi-Zhang (KPZ) theory, we simulated the BD model in one and two dimensions. Effective exponents betaL were obtained in the growth regions, which were rigorously determined for various lengths L. Effective exponents alphaL were obtained from saturation widths in the steady-state regimes. In d=1 we found betaL=beta+AL(-lambda) and alphaL=alpha+BL(-delta), with asymptotic exponents consistent with the KPZ values beta=1/3 and alpha=1/2, and correction-to-scaling exponents 0.2 < or approximately = lambda < or approximately = 0.4 and 0.6 < or approximately = delta < or approximately = 0.8. These strong finite-size corrections explain the previous discrepancies between numerical estimates for BD and the exact KPZ results. In d=2 we could only obtain reliable estimates of alphaL, which are consistent with KPZ values if finite-size corrections with delta approximately 0.4 are considered.