Mean Field Cluster approximation scheme for the duplet-creation model with absorbing phase transition

Abstract

We study the nonequilibrium phase transitions in the one-dimensional duplet creation model using the $n-$site approximation scheme. We find the phase diagram in the space of parameters $(γ,D)$, where $γ$ is the particle decay probability and $D$ is the diffusion probability. Through data $(1\leq n \leq 18)$ we show that in the limit $n\rightarrow \infty$ the model presents a continuous transition of active state for inactive state (absorbing state) for any value of $0\leq D \leq1$. In general, we obtain the critical value of $γ$ and the "gap" density in the transition point for single and pair approximation $γ_c(n=1,D)$, $Δρ(n=1,D)$ and $Δρ(n=2,D)$ respectively.