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 $(\gamma ,D)$, where $\gamma$ is the particle decay probability and $D$ is the diffusion probability. Through data $(1\le n\le 18)$ we show that in the limit $n\to \infty$ the model presents a continuous transition of active state for inactive state (absorbing state) for any value of $0\le D\le 1$. In general, we obtain the critical value of $\gamma$ and the "gap" density in the transition point for single and pair approximation ${\gamma }_c(n=1,D)$, $\Delta \rho (n=1,D)$ and $\Delta \rho (n=2,D)$ respectively.

12 pages, 4 figures