Mean-field analysis of two antiferromagnetically coupled Anderson impurities

We have solved, near $T=0\mathrm{}$, a model describing two magnetic impurities coupled to a band of itinerant electrons and also antiferromagnetically to each other, using an auxiliary-boson mean-field theory which is exact in a large-$N$ limit. Depending upon parameters we find two possible ground states: one in which the Kondo effect occurs and one in which it does not. As the direct antiferromagnetic interaction is varied relative to the Kondo coupling at $T=0\mathrm{}$, a phase transition occurs which may be of first or second order. We compute the low-temperature behavior of the specific heat and the uniform and staggered susceptibility. The nature of the Kondo phase and of the phase transition differ notably from the results found in a recent numerical renormalization-group calculation of a similar model with $N=2\mathrm{}$.