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We simulated a growth model in 1+1 dimensions in which particles areaggregated according to the rules of ballistic deposition with probability p oraccording to the rules of random deposition with surface relaxation (Familymodel) with probability 1-p. For any p>0, this system is in theKardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossoverfrom the Edwards-Wilkinson class (EW) for small p. From the scaling of thegrowth velocity, the parameter p is connected to the coefficient of thenonlinear 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 thegrowth regime as W ~ lambda^beta t^beta, and the scaling of the saturation timeas tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 andstrong corrections to scaling for small lambda. This picture is consistent witha 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. Someconsequences of the slow crossover in this problem are discussed and may helpinvestigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.

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