Properties of the interfaces generated by the competition between stable and unstable growth models

Two different growing mechanisms, given by the Eden model (EM) and the unstable Eden model (UEM), are used to numerically explore the properties of the interface generated by a competitive dynamic process in which particles are aggregated according to the rules of the EM with probability (1-p) and following the UEM with probability p. Based on extensive numerical simulations, it is shown that the interface width exhibits a growing regime that at time t(x2) crosses over to a saturation state such that the width (W-sat) remains stationary. It is shown that W-sat and t(x2) depend on both the lattice size L and the probability p. This behavior can be rationalized by proposing new scaling relationships, which are tested numerically. Furthermore, the relevant exponents are determined showing that the instabilities of the UEM dominate the dynamics of the growing process.