The diagramatical solution of the two-impurity Kondo problem

The problem of the two-impurity Kondo problem is studied via the perturbative diagrammatical method. The high-temperature magnetic susceptibility is calculated to fourth order in the coupling constant J for different regimes. The integral equations for the ground state energy are established and solved numerically. The two-stage Kondo effect and corresponding energy scales are found which agree with the scaling results.