# Local persistence in directed percolation - Condensed Matter > Statistical Mechanics

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Abstract: We reconsider the problem of local persistence in directed site percolation.We present improved estimates of the persistence exponent in all dimensionsfrom 1+1 to 7+1, obtained by new algorithms and by improved implementations ofexisting ones. We verify the strong corrections to scaling for 2+1 and 3+1dimensions found in previous analyses, but we show that scaling is much bettersatisfied for very large and very small dimensions. For d > 4 d is the spatialdimension, the persistence exponent depends non-trivially on d, in qualitativeagreement with the non-universal values calculated recently by Fuchs {\it etal.} J. Stat. Mech.: Theor. Exp. P04015 2008. These results are mainlybased on efficient simulations of clusters evolving under the time reverseddynamics with a permanently active site and a particular survival conditiondiscussed in Fuchs {\it et al.}. These simulations suggest also a new criticalexponent $\zeta$ which describes the growth of these clusters conditioned onsurvival, and which turns out to be the same as the exponent, \eta+\delta instandard notation, of surviving clusters under the standard DP evolution.

Autor: Peter Grassberger

Fuente: https://arxiv.org/