Finite-size scaling study of the ballistic deposition model in (1+1)-dimensions

Abstract

We performed extensive Monte Carlo simulations of the ballistic deposition model in (1 + 1)-dimensions for several system sizes up to 1280 lattice constants, on the square lattice. Though the ballistic deposition model is generally accepted to belong to the Kardar Parisi-Zhang (KPZ) universality class, strong corrections to scaling prevent numerical estimates of the exponents close to the asymptotic values. We obtained a ³ 0.40, b ³ 0.30, and z ³ 1.16, which are consistent with the expected KPZ values of a = 1/2, b = 1/3, and z = 3/2. We found a slow, and even non monotonic, convergence of the exponents towards the asymptotic values, which corroborates previous claims in the literature of strong corrections to scaling.