No abstract

No abstract

By the use of Monte Carlo simulation we study the critical behavior of a three-dimensional stochastic lattice model describing a diffusive epidemic propagation process. In this model, healthy (A) and sick (B) individuals diffuse on the lattice with diffusion constants d A and d B , respectively, and undergo reactions B → A and A + B → 2B. We determine the absorbing phase transition between a steady reactive state and a vacuum state. We obtained the order parameter, order parameter fluctuations, correlation length and their critical exponents by the use of steady state and short-time dynamics simulations. We studied three different diffusion regimes: the case of species A diffusing much slower than species B (d A ≪ d B ), the case of species with equal diffusion constants (d A = d B ) and the case of species A diffusing much faster than species B (d A ≫ d B ). We found only second order transition for all three cases. We did not identify any signal of first order transition for the case d A > d B as predicted by field theory in first order approximation.

We study a stochastic lattice model with parity-conserving particle process using a Monte Carlo procedure. We perform simulations on a Sierpinski carpet fractal with dimension D f = ln 8/ ln 3. We calculate the critical exponents at the threshold of the absorbing phase transition at the known value for the critical diusion p c = 1 (Cardy and Tauber 1996 Phys. Rev. Lett. 77 4780). Using finite-size and finite-time scaling analysis we calculate the critical exponents at p c = 1 and below, where a finite density of particles is found in the long-time limit. From dynamic simulations we calculate the dynamical exponents Z, δ, ν , ν ⊥ and γ , /Zν ⊥ , and they are found to dier from the mean-field values, as well as the stationary exponent β. We check the consistence of the results with the hyperscaling relation.