Asymmetric directed percolation on the square lattice

The author considers directed percolation on the square lattice, with probability p H (p V ) for the horizontal (vertical) bonds to be unbroken. For p H =1- epsilon ( epsilon small) and p V > 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 p H the percolation threshold p V,c ( epsilon ), defined by phi + = phi - at p V =p V,c is also calculated.