Eur. Phys. J. B 5, 257-264 (1998)
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

Abstract

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).