First-order phase transition in a nonequilibrium growth process

We introduce a simple continuous model for nonequilibrium surface growth. The dynamics of the system is defined by the Kardar-Parisi-Zhang equation with a Morse-like potential representing a short range interaction between the surface and the substrate. The mean field solution displays a nontrivial phase diagram with a first-order transition between a growing and a bound surface, associated with a region of coexisting phases, and a tricritical point where the transition becomes second order. Numerical simulations in three dimensions show quantitative agreement with mean field results, and the features of the phase space are preserved even in two dimensions.