Non-equilibrium phase diagram for a model with coalescence, evaporation   and deposition
  We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all dimensions d greater or equal to one between a growing phase, in which the expected mass is infinite at each site, and an exponential phase in which the expected mass is finite. We establish rigorous upper and lower bounds on the critical curve describing the phase transition for this system, and some asymptotics for large or small deposition rates. 
Colm Connaughton, R. Rajesh, Roger Tribe and Oleg Zaboronski
math.PR cond-mat.stat-mech