The nature of the absorbing-state phase transition in the diffusive epidemic process

In the diffusive epidemic process (DEP), particles of two species (A and B) hop on a lattice and undergo reactions B --> A and A + B --> 2B; the B-free state is absorbing. Renormalization group analysis predicts a continuous phase transition to the absorbing state when the hopping rate of B particles, D(B), is greater than or equal to that of A particles, and a discontinuous transition for D(A) > D(B). Monte Carlo simulations of the one-dimensional DEP suggest that, on the contrary, the transition is continuous in all cases. Here we present strong evidence for a continuous transition for D(A) > D(B) in the two-dimensional model as well. Our results suggest that hysteresis is absent in both the one- and two-dimensional cases.