A multilayer contact process

We introduce a contact model with evaporation and deposition of particles at rates p and (1 - p), respectively, per occupied lattice site; while the deposition probability on empty sites depends on the number of occupied nearest-neighbour sites. At large times t this model has three different phases, separated by two critical points (p(1c) = 1/2 and p(2c) = 0.6473 +/- 0.0003). Such phases are: (i) The growth phase (0 less than or equal to p less than or equal to 1/2). Here the mean value of particles per lattice site n and its fluctuations w always increase as time increases. However, two different regimes can be observed, that is n similar to t and w similar to t(1/2), for 0 less than or equal to p < 1/2; while just at p(1c) one has n similar to w similar to t(1/2). (ii) The steady-state phase (1/2 < p < p(2c)), in which n and w reach finite non trivial (n > 0 and w > 0) values, but both quantities diverge for p --> 1/2(+) as (p - 1/2)(-1). (iii) The inactive (or vacuum) state (p(2c) less than or equal to p less than or equal to 1), for which n = 0. At p(2c) the system exhibits an irreversible phase transition which belongs to the universality class of directed percolation model, so for p --> p(2c)(-), n similar to (p(2c) - p)(beta 2) and w similar to (p(2c) - p)(beta 2/2), with beta(2) similar or equal to 0.277. Transitions between phases are continuous, however, the transition at p(1c) (p(2c)) is reversible (irreversible), respectively.