RKKY interactions in the regime of strong localization

We study the influence of strong nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between diluted magnetic moments in metals. We find that the probability distribution for the RKKY interactions assumes strongly non-Gaussian form featuring long tails. Since such distributions cannot be characterized by its moments, we define a $\mathit{\text{typical}}$ value of the interaction amplitude, which we find to be exponentially suppressed in presence of Anderson localization. Our results present a plausible and physically transparent picture describing how Anderson localization effectively eliminates the long range nature of the RKKY interactions.