Mean-Field Cluster Approximation Scheme for the Pair-Creation Model with Absorbing Phase Transition

We study the non-equilibrium phase transitions in the one-dimensional pair-creation model (2A -> 3A, A -> 0) using the n-site approximation scheme. We find the phase diagram in the space of the parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability. Through data (1 <= n <= 18), we show that in the limit n -> infinity the model presents a continuous transition from active state to absorbing state for any value of 0 <= D <= 1. This result is in contrast with that of Fiore and de Oliveira (Phys. Rev. E 70, 046131, 2004) who found a discontinuous transition at high diffusion regime through conserved order parameter simulations.