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

## TL;DR

This paper investigates the phase transitions in a one-dimensional duplet creation model using an n-site approximation, revealing a continuous transition to an absorbing state across various parameters and approximations.

## Contribution

It introduces a mean field cluster approximation scheme for the duplet creation model and analyzes its phase diagram, extending to large cluster sizes to identify transition behavior.

## Key findings

- The model exhibits a continuous phase transition for all diffusion probabilities D.
- Critical values of particle decay probability γ are determined for different cluster sizes.
- The transition point's gap density is quantified for single and pair approximations.

## 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 $(1\leq n \leq 18)$ 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 $\gamma$ 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.