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

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 nu(perpendicular to)approximate to 0.61(6), in agreement with nu(perpendicular to) = 2/D. Also, for this diffusion regime, we estimate beta/nu(perpendicular to) = 1.48, very close to the E expansion prediction beta/nu(perpendicular to) = D-epsilon/8/2 (epsilon = 4 - D) for the regime of equally diffusing particles. (C) 2018 Elsevier B.V. All rights reserved.