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 \(\). Extensive numerical simulations are performed in order to determine the density exponent \(\)and the correlation length exponents \(\) and \(\)for various values of \(\). We observe that these exponents vary continuously with \(\), in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.