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 $1/r^{d+\sigma }$. 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.

RevTeX, 9 pages, including 6 eps-figures

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