Backbends in directed percolation

Abstract

When directed percolation in a bond percolation process does not occur any path to innity on the open bonds will zigzag back and forth through the lattice Backbends are the portions of the zigzags that go against the percolation direction They are important in the physical problem of particle transport in random media in the presence of a eld as they act to limit particle ow through the medium The critical probability for percolation along directed paths with backbends no longer than a given length n is dened as pn We prove that pn is strictly decreasing and converges to the critical probability for undi rected percolation pc We also investigate some variants of the basic model such as by replacing the standard ddimensional cubic lattice with a d dimensional slab or with a Bethe lattice and we discuss the mathematical consequences of alternative ways to formalise the physical concepts of percolation and backbend