Kinetic roughening phase transition in surface growth: Numerical study and mean-field approach

Numerical simulations are reported on a ballistic deposition model that interpolates between the weak- and strong-coupling limits of the stochastic Burgers equation introduced by M. Kardar, G. Parisi, and Y. C. Zhang [Phys. Rev. Lett. 56, 889 (1986)]. The model, which is built on a d-dimensional cubic lattice, considers a random deposition of two kinds of particles, with concentrations c and 1-c, that stick to the deposit or may slide on it by no more than one lattice spacing. Evidence is given for the existence of a phase transition, when varying c, in d=3 and 4, but not in d=2, in agreement with an analytical prediction due to Halpin-Healy [Phys. Rev. Lett. 62, 442 (1989)]. The transition is investigated by analyzing, as a function of c, the scaling exponents of the surface thickness as well as the compactness of the bulk of the deposit. An analytical mean-field approach is proposed that describes most of the features of the phase transition.