Persistence as Order Parameter in Generalized Pair Contact Process with Diffusion

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.