Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

TL;DR

This paper uses cluster mean-field approximations and the coherent anomaly method to analyze the critical behavior of the driven pair contact process with diffusion, revealing differences in true critical scaling between related models.

Contribution

It extends cluster mean-field analysis up to 13 clusters and applies the coherent anomaly method to distinguish true critical behavior in DPCPD and PCPD.

Findings

Critical points estimated accurately and agree with recent simulations.

DPCPD and PCPD share mean-field critical behavior but differ in true critical scaling.

Critical exponents for key quantities are well estimated for DPCPD.

Abstract

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.