Springer LINK: The European Physical Journal B - Abstract Volume 5 Issue 2 (1998) pp 257-264

The European Physical Journal B

ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)

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Abstract Volume 5 Issue 2 (1998) pp 257-264

Numerical study of local and global persistence in directed percolation

H. Hinrichsen (1) (a), H.M. Koduvely (2)

(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

Received: 15 December 1997 / Revised: 6 April 1998 / Accepted: 29 May 1998

Abstract: The local persistence probability P_l(t) that a site never becomes active up to time t, and the global persistence probability P_g(t) that the deviation of the global density from its mean value $\rho(t)-\langle \rho(t) \rangle$ 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, P_l(t) decays algebraically with the exponent $\theta_l \approx 1.50(2)$. The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting $\theta_l$ is an universal exponent. The global persistence exponent $\theta_g$ is found to be equal or larger than $\theta_l$. This contrasts with previously known cases where $\theta_g < \theta_l$. It is shown that in the special case of directed-bond percolation, P_l(t) 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

(a) email: hinrichs@mpipks-dresden.mpg.de

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