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 KPZ equation with a Morse-like potential representing a short range interaction between the surface and the substrate. The mean field solution displays a non trivial 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 3 dimensions show quantitative agreement with mean field results, and the features of the phase space are preserved even in 2 dimensions.