Theory of high-field magnetotransport in a percolating medium

The critical behavior of magnetotransport in a percolating medium in the presence of a magnetic field H of arbitrary strength is discussed. A discrete network model is used to solve the problem exactly for a three-dimensional Sierpinski-gasket fractal, and to perform a direct Monte Carlo simulation of a percolating medium. A very efficient algorithm is used to calculate transport properties in the vicinity of the percolation threshold. We find that there is strong magnetoresistance near the percolation threshold. We also find a different scaling behavior of the effective Ohmic resistivity ρ⁽ᵉ⁾(p,H) and Hall coefficient RH⁽ᵉ⁾(p,H) as functions of the concentration p and magnetic field H. This scaling is due to the appearance of a field-dependent length---the magnetic correlation length ξH. In a percolating metal-insulator mixture, the resistivity ratio with and without a field ρ⁽ᵉ⁾(p,H)/ρ⁽ᵉ⁾(p,0) is predicted to saturate as p{→}pc at a value that is proportional to H3.1.