Duality Transformations for Two-Dimensional Directed Percolation and Resistance Problems

It is shown that the percolation problem with blocked, one-way, or two-way bonds is self-dual on a square lattice. The usual directed percolation (blocked or one-way bonds) is dual to a simpler process with one- or two-way bonds. The results of a Monte Carlo simulation of the latter are reported and an improved bound on the critical probability is derived. The corresponding resistance problem in which circuit elements have different forward and backward resistances is also shown to be self-dual.