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^-1Lᶻ, 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 tc~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.