Dynamic properties in a family of competitive growing models

HOROWITZ, C; EZEQUIEL V ALBANO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Lugar: Ridge, New York.; Año: 2006 vol. 73 p. 8 - 8

1063-651X

The properties of a wide variety of growing models, generically called X-RD, involving the deposition of particles according to competitive processes, such that a particle is attached to the aggregate with probability p following the mechanisms of a generic model X that provides the correlations and at random [random deposition (RD)] with probability (1–p), are studied by means of numerical simulations and analytic developments. The study comprises the following X models: Ballistic deposition, random deposition with surface relaxation, Das Sarma–Tamboronea, Kim-Kosterlitz, Lai–Das Sarma, Wolf-Villain, large curvature, and three additional models that are variants of the ballistic deposition model. It is shown that after a growing regime, the interface width becomes saturated at a crossover time (tx2) that, by fixing the sample size, scales with p according to tx2(p)p–y (p>0), where y is an exponent. Also, the interface width at saturation (Wsat) scales as Wsat(p)p– (p>0), where  is another exponent. It is proved that, in any dimension, the exponents and y obey the following relationship: =yβRD, where βRD=1/2 is the growing exponent for RD. Furthermore, both exponents exhibit universality in the p0 limit. By mapping the behavior of the average height difference of two neighboring sites in discrete models of type X-RD and two kinds of random walks, we have determined the exact value of the exponent . When the height difference between two neighbouring sites corresponds to a random walk that after walking <n> steps returns to a distance from its initial position that is proportional to the maximum distance reached (random walk of type A), one has =1/2. On the other hand, when the height difference between two neighboring sites corresponds to a random walk that after <n> steps moves <l> steps towards the initial position (random walk of type B), one has =1. Finally, by linking four well-established universality classes (namely Edwards-Wilkinson, Kardar-Parisi-Zhang, linear [molecular beam epitaxy (MBE)] and nonlinear MBE) with the properties of type Aand B of random walks, eight different stochastic equations for all the competitive models studied are derived.