Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

We simulated a growth model in (1+1) dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient λ of the nonlinear term of the KPZ equation, giving λ∼p^γ, with γ=2.1±0.2. Our numerical results confirm the interface width scaling in the growth regime as W∼λ^βt^β and the scaling of the saturation time as τ∼λ^-1L^z, with the expected exponents β=1/3 and z=3/2, and strong corrections to scaling for small λ. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c∼λ^-4∼p^-8, in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.