Critical behavior of a one-dimensional diffusive epidemic process

We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants D-A and D-B, respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases D-A=D-B and D-AD-B. In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension d=1. Our results show no signature of a first-order transition in the case of D-A >D-B. A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent nu =2 as predicted by field-theoretical arguments. Estimates for beta/nu are given for all relevant regimes.