Pair contact process with diffusion: field theory

TL;DR

This paper attempted a field-theoretic analysis of the pair contact process with diffusion using renormalization group methods but was withdrawn due to unphysical results, highlighting ongoing challenges in modeling this system.

Contribution

The authors conducted a renormalization group analysis of the PCPD but withdrew the work after identifying unphysical implications, emphasizing the difficulty of a consistent analytical approach.

Findings

Identified a nontrivial RG fixed point

Found fluctuations of total particles to be negative

Concluded the analysis was inconsistent and invalid

Abstract

This paper, which was concerned with a field-theoretic analysis of the PCPD by means of the renormalization group, has been withdrawn by the authors. We had found a nontrivial RG fixed point, but could not exclude the possibility that it was outside the basin attraction of the RG flow initial conditions. A benevolent, yet careful and critical reader, H.K. Janssen, kindly provided us with an argument showing that our fixed point actually led to unphysical consequences: Given the critical exponents we computed, the fluctuations of the total number of particles would be negative at large times close to the critical point. This renders our contribution inconsistent and thus invalid. Hence we have decided to withdraw our paper from the archive. A consistent analytical description of the PCPD unfortunately remains a challenge.