## Magnetoresistance of Three-Constituent Composites: Percolation Near a
Critical Line

#### Sergey V. Barabash[1], David J. Bergman[1,2], and D. Stroud[1],
[1] Department of Physics, The Ohio State University, Columbus, Ohio 43210;
[2] School of Physics and Astronomy, Tel Aviv University, Ramat Aviv,
Israel

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 nonsaturating magnetoresistance. The percolation problem which describes
this line is a generalization of anisotropic percolation. We locate the
percolation threshold and determine that t = s = 1.30 +/- 0.02 and that
nu = 4/3 +/- 0.02, which are the same values 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.