A precise approximation for directed percolation in d=1+1
Statistical Mechanics
2009-11-07 v2 Cellular Automata and Lattice Gases
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).
Keywords
Cite
@article{arxiv.cond-mat/0205490,
title = {A precise approximation for directed percolation in d=1+1},
author = {Clément Sire},
journal= {arXiv preprint arXiv:cond-mat/0205490},
year = {2009}
}
Comments
4 pages, 3 EPS figures; Submitted to Physical Review Letters v2: minor typos + 1 major typo in Eq. (30) corrected