Numerical Study of Local and Global Persistence in Directed Percolation

Details Numerical Study of Local and Global Persistence in Directed Percolation Numerical Study of Local and Global Persistence in Directed Percolation

1997-11-27

arxiv.org/abs/cond-mat/9711287v1

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

Physics

Condensed Matter

Statistical Mechanics

revtex, 7 pages, including 6 eps figures

Scientific paper

10.1007/s100510050443

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)-<\rho(t)> does not change its sign up to time t are studied in a one-dimensional directed percolation process by Monte Carlo simulations. At criticality, starting from random initial conditions, both P_l(t) and P_g(t) decay algebraically with exponents theta_l ~ theta_g ~ 1.50(2), which is in contrast to previously known cases where theta_g < theta_l. The exponents are found to be independent of the initial density and the microscopic details of the dynamics, suggesting that theta_l and theta_g are universal exponents. 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).

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