Condensation and evaporation on a randomly occupied square lattice

We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for "growing" and "culling" of particles. In one version we allow the particles to move laterally along the surface (mobile layer) and in the other version this motion is not allowed (immobile case). In the former case, both analytical and computer simulation results are presented, while in the latter only simulation is possible. We introduce growth and culling probabilities appropriate for condensation and evaporation on a two-dimensional surface, and compare results with existing models for this problem. Our results show a very interesting behavior under certain conditions that are quite different from earlier models. We find a possibility of hysteresis not reported earlier for such models.