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

The contact process with diffusion (PCPD) defined by the binary reactions B+B→B+B+B, B+B→0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition. Multiple studies indicated that further coarse-graining of the model may be needed for its effective long-time, large-scale description. We introduce a two-species representation for the PCPD in which single particles B and particle pairs A are dynamically coupled according to the stochastic reaction processes B+B→A, A→A+B, A→0, and A→B+B, with each particle type diffusing independently. Mean-field analysis reveals that the phase transition of this model is driven by competition and balance between the two species. We employ Monte Carlo simulations in one, two, and three dimensions to demonstrate that this model consistently captures the pertinent features of the PCPD and the upper critical dimension is dc=2. The extracted moment ratios from our simulations indicate that our model displays the same temporal crossover behavior as the PCPD, which further corroborates its full dynamical equivalence with our coupled model.