  We have carried out a generalized Schrieffer-Wolff transformation of an
Anderson two-impurity Hamiltonian to study the low-energy spin interactions of
the system. The second-order expansion yields the standard Kondo Hamiltonian
for two impurities with additional scattering terms. At fouth-order, we get the
well-known RKKY interaction. In addition, we also find an antiferromagnetic
superexchange coupling and a correlated Kondo coupling between the two
impurities.
