Finite-size Scaling Study of the Ballistic Deposition Model in (1 + 1)-dimensions

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.