A model for anomalous directed percolation

Abstract

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in $d$ spatial dimensions as $1/r^{d+σ}$. Extensive numerical simulations are performed in order to determine the density exponent $β$ and the correlation length exponents $ν_{||}$ and $ν_\perp$ for various values of $σ$. We observe that these exponents vary continuously with $σ$, in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.