Absence of two energy scales in the two-impurity Kondo model

It is believed that the successive antiferromagnetic scattering of the conduction electrons on two magnetic impurities in a metal, induces a magnetic interaction between the impurities which sets an energy scale for the system, in addition to the Kondo temperature. However, it is shown here that this contradicts a scaling law for the two-impurity Anderson model in the magnetic limit which becomes exact for a large bandwidth.