Dynamical mean-field approximation for pair contact process with a particle source

TL;DR

This study uses dynamical mean-field approximations to analyze the pair contact process with a particle source, revealing critical behavior and phase transition properties in one dimension.

Contribution

It applies high-level cluster mean-field approximations up to 12 sites to accurately analyze the critical behavior of the process, challenging previous predictions.

Findings

Critical point shows a vanishing discontinuity with increasing cluster size.

Order parameter and isolated particle density share the same critical behavior.

No critical behavior in the inactive phase contrary to earlier predictions.

Abstract

The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially for $n \ge 6$ and allow us to derive reliable extrapolations to the limit $n \to \infty$. At the zero source limit, the critical point exhibits a discontinuity whose magnitude vanishes with $1/n$. The coherent anomaly analysis of data supports that the vanishing of order parameter and density of isolated particles has the same critical behavior. In contrast to an earlier prediction, the present approximation does not support the existence of critical behavior in the inactive phase where the frozen density of isolated particles depends on the initial state.