Pair Contact Process with Diffusion: Failure of Master Equation Field Theory

TL;DR

This paper shows that the microscopic field theory derived from the master equation fails to describe the critical behavior of the Pair Contact Process with Diffusion, indicating the need for a more coarse-grained approach.

Contribution

It demonstrates the failure of the direct microscopic field theory to capture the phase transition in PCPD, highlighting the necessity for an alternative effective field theory.

Findings

No stable fixed point in the accessible parameter region.

Predicted particle anticorrelations contradict positivity of fluctuations.

Microscopic field theory does not adequately describe the critical behavior.

Abstract

We demonstrate that the `microscopic' field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.