Crossover from the pair contact process with diffusion to directed percolation

TL;DR

This paper investigates the transition behaviors from the pair contact process with diffusion (PCPD) and driven PCPD to directed percolation (DP) in one dimension, revealing non-DP critical scaling and mean-field tricritical behavior.

Contribution

It provides numerical estimates of crossover exponents and demonstrates the non-DP nature of PCPD critical scaling, along with confirming the mean-field prediction for DPCPD.

Findings

Crossover exponents estimated as 1/φ ≈ 0.58 for PCPD and 0.49 for DPCPD.

Non-DP critical scaling behavior in PCPD supported by anomalous amplitude scaling.

DPCPD crossover aligns with mean-field tricritical DP class predictions.

Abstract

Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The crossover exponents $\phi$ are estimated numerically as $1/\phi \simeq 0.58\pm0.03$ for the PCPD and $1/\phi \simeq 0.49 \pm 0.02$ for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected.