Theory of the many-impurity Kondo effect for weakly interacting impurities

The properties of dilute magnetic alloys which exhibit both a spin-dependent impurity-impurity interaction and the Kondo effect are studied by extending the previous two-impurity calculations of the authors to many impurities. The general formulation of the many-impurity Kondo problem is presented and discussed in the very-low-concentration limit. It is found that the effective Kondo temperature TKE(n) of the impurity at site n is given by TKE(n)=TK[1-(WₙTK)²]1/2, where Wₙ is an effective impurity-impurity interaction potential acting on the site n under consideration and TK is the single-impurity Kondo temperature. For a set of randomly distributed impurities, we find that TKE(n) is a random variable whose value is site dependent. Expressions for the high-temperature resistivity are also obtained.