Variable-range-hopping magnetoresistance

I consider hopping magnetoresistance R of a two-dimensional insulator with small metallic impurities. I prove that if impurity density n is low (${\mathit{na}}_{\mathit{B}}^2$${\mathit{a}}_{\mathit{B}}$ is the impurity Bohr radius), R increases with magnetic field B. If ${\mathit{na}}_{\mathit{B}}^2$>1, then R(B) has a minimum. In both cases, in high magnetic field lnR∝ √B/T , with the dependence on temperature T characteristic of one-dimensional hopping.