  The quantum phase diagram of disordered electron systems as function of the
concentration of magnetic impurities nm and the local exchange coupling J is
studied in the dilute limit. We take into account the Anderson localisation of
the electrons by a nonperturbative numerical treatment of the disorder
potential. The competition between RKKY interaction JRKKY and the Kondo effect,
as governed by the temperature scale TK, is known to gives rise to a rich
magnetic quantum phase diagram, the Doniach diagram. Our numerical calculations
show that in a disordered system both the Kondo temperature TK and JRKKY are
widely distributed. Accordingly, also their ratio, JRKKY /TK is widely
distributed as shown in Fig. 1 (a). However, we find a sharp cutoff of that
distribution, which allows us to define a critical density of magnetic
impurities nc below which Kondo screening wins at all sites of the system above
a critical coupling Jc, forming the Kondo phase[see Fig. 1 (b)]. As disorder is
increased, Jc increases and a spin coupled phase is found to grow at the
expense of the Kondo phase. From these distribution functions we derive the
magnetic susceptibility which show anomalous power law behavior. In the Kondo
phase that power is determined by the wide distribution of the Kondo
temperature, while in the spin coupled phase it is governed by the distribution
of JRKKY. At low densities and small J < Jc we identify a paramagnetic phase.
We also report results on a honeycomb lattice, graphene, where we find that the
spin coupled phase is more stable against Kondo screening, but is more easily
destroyed by disorder into a PM phase.
