Exact results in the theory of magnetic alloys

Recently it has been shown that many traditional models used for a description of dilute magnetic alloys are completely integrable and may be solved exactly without any approximation. In this article we summarize the results which have been obtained in this way.

The main part of the article is devoted to the consistent and detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-d model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model. The thermodynamic properties of a magnetic impurity in a non-magnetic metal host obtained by the Bethe method are considered in detail. Mainly attention is paid to the analysis of singularities associated with the formation of a localized moment, Kondo effect and mixedvalence phenomenon, which can be treated analytically.

In the introductory part of the article we discuss the applicability of the models which we study in the paper to the real alloys and consider some modern experimental data which give the evidence of the many-body effects in dilute magnetic alloys. A brief review of some theoretical results which have been obtained using alternative approaches is given. We think that these results illustrate some features of the exact solution.

This review was completed in June 1982.