Oriented bond percolation

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Abstract
Percolation with bonds oriented along an external field direction is considered. Assuming that the second-order type phase transition picture can be applied in the vicinity of the critical point the threshold probability and the correlation length exponent nu 0 is calculated on the square lattice by Monte Carlo techniques using finite-size scaling arguments. It is found that nu 0=1.65+or-0.06, i.e. the orientated percolation belongs to a different university class from the unorientated one. The critical probabilities for several two-dimensional lattices are determined.