B. Spivak et al., MAGNETIC-FIELD DEPENDENCE OF THE LOCALIZATION LENGTH ON THE DIELECTRIC SIDE OF METAL-INSULATOR TRANSITIONS, JETP letters, 59(9), 1994, pp. 628-634
Magnetic field dependence of negative magnetoresistance (MR) in variab
le-range-hopping conduction is discussed. Above four dimensions, the n
egative MR saturates at large magnetic fields. In dimensions lower tha
n four, the negative MR corresponds to a field-dependent correction to
the localization length. A qualitative coarse-graining picture is pre
sented for such behavior.