Accuracy of the cluster-approximation method in a nonequilibrium model

TL;DR

This paper evaluates the accuracy of the cluster-approximation method in predicting critical points of a nonequilibrium phase transition, finding excellent agreement with simulations for continuous transitions in 1+1 dimensions.

Contribution

It demonstrates the effectiveness of the cluster-approximation method in estimating critical points for nonequilibrium phase transitions in one dimension.

Findings

Cluster approximation accurately predicts critical points for continuous transitions.

No first-order transitions observed in 1+1 dimensions, consistent with simulations.

Extrapolations from cluster approximations align well with simulation data.

Abstract

We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and the dimension of the system. Using increasingly large clusters, we use the cluster approximation method to obtain estimates for the critical points in 1+1 dimensions. For the continuous phase transitions only, extrapolations of these approximations show excellent agreement with simulation results. Further, the approximations suggest that, consistent with simulation results, in 1+1 dimensions no first-order phase transitions are observed.