Global Persistence in Directed Percolation

We consider a directed percolation process at its critical point. The probability that the deviation of the global order parameter with respect to its average has not changed its sign between 0 and t decays with t as a power law. In space dimensions d ≥ 4 the global persistence exponent θp that characterizes this decay is θp = 2 while for d < 4 its value is increased to first order in ε = 4 − d. Combining a method developed by Majumdar and Sire [1] with renormalization group techniques we compute the correction to θp to first order in ε. The global persistence exponent is found to be a new and independent exponent. We finally compare our results with existing simulations. PACS 05.40+j L.P.T.H.E. ORSAY 98/26 Laboratoire associé au Centre National de la Recherche Scientifique URA D0063