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 of the nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma = 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-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. 
Anna Chame and Fabio D. A. Aarao Reis