Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models

D. MURACA; L. A. BRAUNSTEIN; R. C. BUCETA

Bangalore

Conferencia; 22nd International Conference on Statistical Physics, STATPHYS 22; 2004

International Union for Pure and Applied Physics (IUPAP) and National Science Seminar Complex, at the Indian Institute of Science

The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability p and the other with probability 1-p. The p−dependance produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in p (or 1-p). We show that the origin of such dependance is the existence of two different average time rates. Thus, the quadratic p-dependance is an universal behavior of all the competitive growth models. We derive analytically the continuous equations for two competitive growth models, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic competitive growth models presented here and with the proposed scalings.