A model for anomalous directed percolation

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 $1/r^{d+\sigma}$. Extensive numerical simulations are performed in order to determine the density exponent $\beta$ and the correlation length exponents $\nu_{||}$ and $\nu_\perp$ for various values of $\sigma$. We observe that these exponents vary continuously with $\sigma$, in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.