A multilayer contact process

MIGUEL LUIS HOYUELOS; EZEQUIEL ALBANO,; HECTOR MÁRTIN,

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

IOP Publishing

Año: 1997 vol. 30 p. 431 - 431

0305-4470

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 (p1c = 1/2 and p2c = 0.6473 ± 0.0003). Such phases are: (i) The growth phase (0 < p < 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 ∼ t and w ∼ t^1/2, for 0 < p < 1/2; while just at p1c one has n ∼ w ∼ t^1/2. (ii) The steady-state phase (1/2 < p < p2c), 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 (p2c < p < 1), for which n = 0. At p2c the system exhibits an irreversible phase transition which belongs to the universality class of directed percolation model, so for p → p2c^-, n ∼ (p2c − p)^β2 and w ∼ (p2c − p)^(β2/2), with β2 \simeq 0.277. Transitions between phases are continuous, however, the transition at p1c (p2c) is reversible (irreversible), respectively.