Local persistence in directed percolation

Abstract

We reconsider the problem of local persistence in directed site percolation. Wepresent improved estimates of the exponent of persistence in all dimensions from1+1 to7+1, obtained using new algorithms and using improved implementationsof existing ones. We verify the strong corrections to scaling for2+1 and3+1 dimensions found in previous analyses, but we show that scaling ismuch better satisfied for very large and very small dimensions. Ford>4 (d is the spatial dimension), the persistence exponent depends non-trivially ond, in qualitative agreement with the non-universal values calculated recently by Fuchs et al (2008J. Stat. Mech. P04015). These results are mainly based on efficient simulations of clusters evolvingunder the time reversed dynamics with a permanently active site and a particular survivalcondition discussed by Fuchs et al. These simulations suggest also a new critical exponentζ whichdescribes the growth of these clusters conditioned on survival, and which turns out to be the same as theexponent, η+δ in standard notation, of surviving clusters under the standard DP evolution.