M Barma and R Ramaswamy 1986 J. Phys. A: Math. Gen. 19 L605 doi:10.1088/0305-4470/19/10/009
M Barma and R Ramaswamy
Show affiliationsJust above the percolation concentration, a path on the backbone which leads from one side of the lattice to the other is not direct by zigzags through the lattice. Backbends are the portions of the zigzags which go backwards. They are important in the problem of particle transport in strong external fields, as they act as traps and limit the current. The threshold concentration for the proliferation of paths with backbends no longer than a given length L is defined as pb(L), with the limits pb(0)=pd (directed percolation) and pb( infinity )=pc (ordinary percolation). The inverse function zeta (p) is the smallest integer such that, for given p between pc and pd, there are paths to infinity on which every backbend is smaller than zeta (p). This minimal backbend length is computed on a Bethe lattice and shown to diverge as (p-pc)-12/. It is argued heuristically that on all lattices zeta (p) is proportional to the correlation length in the limit p to pc. The chemical lengths of minimal backbend paths on the Bethe lattice are calculated.
82B43 Percolation (See also 60K35)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 10 (11 July 1986)
M Barma and R Ramaswamy 1986 J. Phys. A: Math. Gen. 19 L605
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