Anomalies in simulations of nearest neighbor ballistic deposition

摘要

Ballistic Deposition (BD) is a prototypical model for interface growth and for dynamic scaling behavior in non-equilibrium systems. ED is typically investigated with computer simulations where randomness is replaced by the use of deterministic Pseudo Random Number Generators (PRNGs). In this study of ED, several results discrepant with the prevailing paradigm, were observed. First, the value of the roughness exponent, chi, obtained is below the value for a random walk (i.e., chi < 1/2). The value chi 1/2 is predicted by the KPZ equation, and many models of growth obtain this exponent. Second, height fluctuations of the growing interface appear not to satisfy simple scaling. Third, a decrease in the surface roughness is observed in a conjectured steady state regime. Computer implementations of ED may be responsible for the discrepancies. A coupling between the ED algorithm and a PRNG algorithm is identified, and statistically discrepant results are obtained for an implementation with a different PRNG.