  A recently developed self-consistent effective medium approximation, for
composites with a columnar microstructure, is applied to such a
three-constituent mixture of isotropic normal conductor, perfect insulator, and
perfect conductor, where a strong magnetic field {\bf B} is present in the
plane perpendicular to the columnar axis. When the insulating and perfectly
conducting constituents do not percolate in that plane, the
microstructure-induced in-plane magnetoresistance is found to saturate for
large {\bf B}, if the volume fraction of the perfect conductor $p_S$ is greater
than that of the perfect insulator $p_I$. By contrast, if $p_S<p_I$, that
magnetoresistance keeps increasing as ${\bf B}^2$ without ever saturating. This
abrupt change in the macroscopic response, which occurs when $p_S=p_I$, is a
critical point, with the associated critical exponents and scaling behavior
that are characteristic of such points. The physical reasons for the singular
behavior of the macroscopic response are discussed. A new type of percolation
process is apparently involved in this phenomenon.
