A coupled two-species model for the pair contact process with diffusion

The contact process with diffusion (PCPD) defined by the pair reactions 2B→3B, 2B→0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies indicated that further coarse-graining of the model may be needed for its effective long-time, large-scale description. We introduce a coarse-grained two-species representation for the PCPD in which single particles B and particle pairs A are coupled according to the processes 2B→A, A→A+B, A→0, A→2B, with each type of particles diffusing independently. We employ Monte Carlo simulations in one, two, and three dimensions to demonstrate that this model consistently captures the pertinent features of the PCPD. In the inactive phase, A particles die out rapidly, effectively leaving the B species to undergo pure pair annihilation kinetics. At criticality, both A and B densities decay with similar exponents to those measured for the PCPD and display mean-field scaling above the critical dimension d_c=2. In one dimension, exponents for the B species obtained from seed simulations also agree well with previously reported ranges.