Critical behavior of a one-dimensional diffusive epidemic process

Abstract

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 ${D}_{A}<{D}_{B}.$ A first-order transition has been conjectured for ${D}_{A}>{D}_{B}.$ 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 $\ensuremath{\nu}=2$ as predicted by field-theoretical arguments. Estimates for $\ensuremath{\beta}/\ensuremath{\nu}$ are given for all relevant regimes.