  We investigate the effects of nonmagnetic disorder on the
Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying
numerically the Anderson model with on-site and hopping disorder on a honeycomb
lattice at half filling. We evaluate the strength of the interaction as a
function of the distance R between two magnetic ions, as well as their lattice
positions and orientations. In the clean limit, we find that the strength of
the interaction decays as 1/R^3, with its sign and oscillation amplitude
showing strong anisotropy. With increasing on-site disorder, the mean amplitude
decreases exponentially at distances exceeding the elastic mean free path. At
smaller distances, however, the oscillation amplitude increases strongly and
its sign changes on the same sublattice for all directions but the armchair
direction. For random hopping disorder, no sign change is observed. No
significant changes to the geometrical average values of the RKKY interaction
are found at small distances, while exponential suppression is observed at
distances exceeding the localization length.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons