Entropic long-range ordering in an adsorption-desorption model

We examine a two-dimensional nonequilibrium lattice model where particles adsorb at empty sites and desorb when the number of neighbouring particles is greater than a given threshold. In a certain range of parameters the model exhibits entropic ordering similar to some hard-core systems. However, contrary to hard-core systems, upon increasing the density of particles the ordering gets destroyed. In the heterogenous version of our model a regime with slow dynamics appears, that might indicate formation of some kind of glassy structures.