https://doi.org/10.1007/s100510050656
A model for anomalous directed percolation
1
Max-Planck-Institut für Physik komplexer Systeme,
Nöthnitzer Straße 38, 01187 Dresden, Germany
2
CATS, The Niels Bohr Institute, Blegdamsvej 17,
2100 Copenhagen Ø, Denmark
Received:
4
September
1998
Accepted:
22
September
1998
Published online: 15 February 1999
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 β and the correlation length exponents and 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.
PACS: 05.70.Ln – Nonequilibrium thermodynamics, irreversible processes / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999