Asymmetric directed percolation on the square lattice
- 21 February 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (3) , 591-598
- https://doi.org/10.1088/0305-4470/16/3/018
Abstract
The author considers directed percolation on the square lattice, with probability pH(pV) for the horizontal (vertical) bonds to be unbroken. For pH=1- epsilon ( epsilon small) and pV> sigma ( epsilon ) the percolating cluster is asymptotically within a cone phi +< phi < phi +. The author calculates phi +or- and the fluctuations of the boundaries at phi = phi +or- as power series in epsilon , up to terms approximately epsilon 2, showing that the transverse spread of the percolating cluster is random walk-like. For any given pH the percolation threshold pV,c( epsilon ), defined by phi += phi - at pV=pV,c is also calculated.Keywords
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