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
