BALLISTIC DEPOSITION WITH POWER-LAW NOISE - A VARIANT OF THE ZHANG MODEL

We study a variant of the Zhang model [Y.-C. Zhang, J. Phys. (Paris) 51, 2113 (1990)], ballistic deposition of rods with the length l of the rods being chosen from a power-law distribution P(l) approximately l-1-mu. Unlike in the Zhang model, the site at which each rod is dropped is chosen randomly. We confirm that the growth of the rms surface width w with length scale L and time t is described by the scaling relation w(L,t) = L-alpha-w(t/L-alpha/beta), and we calculate the values of the surface-roughening exponents-alpha and beta. We find evidence supporting the possibility of a critical value mu-c almost-equal-to 5 for d = 1, with alpha = 1/2 and beta = 1/3 for mu > mu-c, while for mu < mu-c, alpha and beta vary smoothly, attaining the values alpha = beta = 1 for mu = 2.