https://doi.org/10.1007/s100510050443
Numerical study of local and global persistence in directed percolation
1
Max-Planck-Institut für Physik komplexer
Systeme,
Nöthnitzer Straße 38, 01187 Dresden, Germany
2
Department of Physics of Complex Systems,
Weizmann Institute of Science, Rehovot 76100, Israel
Corresponding author: a hinrichs@mpipks-dresden.mpg.de
Received:
15
December
1997
Revised:
6
April
1998
Accepted:
29
May
1998
Published online: 15 September 1998
The local persistence probability that a site never
becomes active up to time t, and the global persistence probability
that the deviation of the global density from its mean value
does not change its sign up to
time t are studied in a (1+1)-dimensional directed percolation process
by Monte-Carlo simulations. At criticality, starting from random
initial conditions,
decays algebraically
with the exponent
. The value is
found to be independent of the initial density and the microscopic
details of the dynamics, suggesting
is an universal
exponent. The global persistence exponent
is found
to be equal or larger than
. This contrasts with
previously known cases where
. It is shown that in
the special case of directed-bond percolation,
can be related
to a certain return probability of a directed percolation process with
an active source (wet wall).
PACS: 64.60.Ak – Renormalization-group, fractal and percolation studied of phase transition / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.70.Ln – Nonequilibrium thermodynamics, irreversible processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998