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

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

2002-05-23

arxiv.org/abs/cond-mat/0205490v2

Phys. Rev. E 66, 066128 (2002)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.66.066128

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).

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