Dynamical mean-field approximations for a diffusive pair contact process

TL;DR

This paper uses advanced dynamical mean-field approximations to analyze phase transitions in a diffusive pair contact process across various dimensions, revealing diffusion rate independence and potential universality of critical exponents.

Contribution

It extends mean-field approximations up to 18-site clusters and applies the coherent anomaly method to explore critical behavior in different dimensions.

Findings

Critical $eta$ exponent is independent of diffusion rate.

Higher-dimensional approximations suggest a universal set of critical exponents.

Mean-field approach effectively captures phase transition characteristics.

Abstract

Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional model. The application of coherent anomaly method shows that the critical $\beta$ exponent does not depend on the strength of diffusion rate. The extension of the mean-field approximation to higher dimensions also suggests that the critical behavior may be described by a unique set of exponents.