Persistence as Order Parameter in Generalized Pair Contact Process with Diffusion

TL;DR

This study investigates the persistence behavior in the generalized pair contact process with diffusion (GPCPD), revealing critical scaling laws and universality class characteristics that interpolate between directed percolation and PCPD.

Contribution

It introduces an analysis of persistence as an order parameter in GPCPD, providing new insights into its critical behavior and universality class transition.

Findings

Persistence transition coincides with density transition

Finite size and off-critical scaling laws are established

Correlation-time exponent matches directed percolation class

Abstract

The question of universality class of pair contact process with diffusion (PCPD) is revisited with an alternative approach. We study persistence in Generalized Pair-Contact Process with diffusion (GPCPD) introduced by Noh and Park, (Phys. Rev. E 69,016122(2004)). This model allows us to interpolate between directed percolation (DP) and PCPD universality classes. We find that transition to nonzero persistence is at same parameter value as transition to zero number density. We obtain finite size scaling and off-critical scaling collapse for persistence and find critical exponents by fitting phenomenological scaling laws to persistence. While the dynamic scaling exponent $z$ varies continuously in GPCPD, the correlation-time exponent $\nu_\parallel$ matches with directed percolation universality class.