Persistence as the order parameter in a generalized pair-contact process with diffusion

The question of the universality class of the pair-contact process with diffusion (PCPD) is revisited with an alternative approach. We study persistence in a generalized pair-contact process with diffusion (GPCPD) introduced by Noh and Park (2004 Phys. Rev. E 69 016122). This model allows us to interpolate between directed percolation (DP) and PCPD universality classes. We find that the transition to nonzero persistence is at the same parameter value as the transition to zero number density. We obtain the finite-size scaling and off-critical scaling collapse for persistence and find the 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 the DP universality class. (paper: classical statistical mechanics, equilibrium and non-equilibrium)