  The silver chalcogenides provide a striking example of the benefits of
imperfection. Nanothreads of excess silver cause distortions in the current
flow that yield a linear and non-saturating transverse magnetoresistance (MR).
Associated with the large and positive MR is a negative longitudinal MR. The
longitudinal MR only occurs in the three-dimensional limit and thereby permits
the determination of a characteristic length scale set by the spatial
inhomogeneity. We find that this fundamental inhomogeneity length can be as
large as ten microns. Systematic measurements of the diagonal and off-diagonal
components of the resistivity tensor in various sample geometries show clear
evidence of the distorted current paths posited in theoretical simulations. We
use a random resistor network model to fit the linear MR, and expand it from
two to three dimensions to depict current distortions in the third (thickness)
dimension. When compared directly to experiments on Ag$_{2\pm\delta}$Se and
Ag$_{2\pm\delta}$Te, in magnetic fields up to 55 T, the model identifies
conductivity fluctuations due to macroscopic inhomogeneities as the underlying
physical mechanism. It also accounts reasonably quantitatively for the various
components of the resistivity tensor observed in the experiments.
