Model for a macroscopically disordered conductor with an exactly linear high-field magnetoresistance

We calculate the effective resistivity of a macroscopically disordered two-dimensional conductor consisting of two components in a perpendicular magnetic field. When the two components have equal area fractions, we use a duality theorem to show that the magnetoresistance is nonsaturating and at high fields varies exactly linearly with the magnetic field. At other compositions, an effective-medium calculation leads to a saturating magnetoresistance. We briefly discuss possible connections between these results and magnetoresistance measurements on heavily disordered chalcogenide semiconductors.