We present a large-N variational approach to describe the magnetism of
insulating doped semiconductors based on a disorder-generalization of the
resonating-valence-bond theory for quantum antiferromagnets. This method
captures all the qualitative and even quantitative predictions of the
strong-disorder renormalization group approach over the entire experimentally
relevant temperature range. Finally, by mapping the problem on a hard-sphere
fluid, we could provide an essentially exact analytic solution without any
adjustable parameters.Comment: 5 pages, 3 eps figure
