Numerical Study of Local and Global Persistence in Directed Percolation

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)-<ρ(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).