Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line
Sergey V. Barabash, David J. Bergman, D. Stroud
Abstract
Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is found to have a critical line which separates regions of saturating and non-saturating magnetoresistance. The percolation problem which describes this line is a generalization of anisotropic percolation. We locate the percolation threshold and determine the t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in two-constituent 2D isotropic percolation. We also determine the exponents which characterize the critical dependence on magnetic field, and confirm numerically that nu is independent of anisotropy. We propose and test a complete scaling description of the magnetoresistance in the vicinity of the critical line.
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