Stationary and dynamical critical behavior of the three-dimensional Diffusive Epidemic Process

Abstract

We investigate the critical behavior of a stochastic lattice model describing the hopping of two species that undergo reactions B→A and A+B→2B. We simulate the model defined on a 3D lattice and determine the threshold of the absorbing phase transition to the state at which species B is extinct. Using steady state and short-time dynamics simulations, we calculate the order parameter, order parameter fluctuations, correlation length and their critical exponents. We focus in the case of species A diffusing much faster than species B. We did not find signatures of a first-order transition that has been conjectured in the literature. We report a continuous transition with the perpendicular correlation exponent ν⊥≈0.61(6), in agreement with ν⊥=2∕D. Also, for this diffusion regime, we estimate β∕ν⊥=1.48, very close to the ϵ expansion prediction β∕ν⊥=D−ε∕82 (ε=4−D) for the regime of equally diffusing particles.