  Magnetic impurities embedded in a metal interact via an effective
Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling mediated by the conduction
electrons, which is commonly assumed to be long ranged, with an algebraic decay
in the inter-impurity distance. However, they can also form a Kondo screened
state that is oblivious to the presence of other impurities. The competition
between these effects leads to a critical distance above which Kondo effect
dominates, translating into a finite range for the RKKY interaction. We study
this mechanism on the square and cubic lattices by introducing an exact mapping
onto an effective one-dimensional problem that we can solve with the density
matrix renormalization group method (DMRG). We show a clear departure from the
conventional RKKY theory, that can be attributed to the dimensionality and
different densities of states. In particular, for dimension d>1, Kondo physics
dominates even at short distances, while the ferromagnetic RKKY state is
energetically unfavorable.
