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 α⩾0.40, β⩾0.30, and z⩾1.16, which are consistent with the expected KPZ values of α=1/2, β=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.