Backbends in directed percolation

نویسندگان

  • Rahul Roy
  • Anish Sarkar
چکیده

When directed percolation in a bond percolation process does not occur, any path to innnity 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 deened as p n. We prove that (p n) is strictly decreasing and converges to the critical probability for undi-rected percolation p c. We also investigate some variants of the basic model, such as by replacing the standard d-dimensional cubic lattice with a (d ? 1)-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'. Acknowledgments We thank Ronald Meester and Ramakrishna Ramaswamy for many helpful discussions. Sarkar and White thank everyone at the Indian Statistical Institute in New Delhi for their kind hospitality.

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تاریخ انتشار 1997