A precise approximation for directed percolation in d=1+1

Abstract

We introduce an approximation specific to a continuous model for directed percolation, which is strictly equivalent to 1+1 dimensional directed bond percolation. We find that the critical exponent associated to the order parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in remarkable agreement with the best current numerical estimate beta=0.276486(8).

4 pages, 3 EPS figures; Submitted to Physical Review Letters v2: minor typos + 1 major typo in Eq. (30) corrected

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