Impurity correlations in dilute Kondo alloys

TL;DR

This paper investigates the validity of the single impurity Kondo model in dilute alloys by developing a virial expansion and analyzing impurity correlations, revealing potential singularities in heat capacity at second order.

Contribution

It introduces a virial expansion approach to quantify impurity correlations in dilute Kondo alloys, extending understanding beyond the single impurity approximation.

Findings

Derived the second-order impurity density term from the 2-impurity Kondo problem.

Identified potential singularities in heat capacity due to impurity correlations.

Provided criteria for the dilute limit where the single impurity model remains valid.

Abstract

The single impurity Kondo model is often used to describe metals with dilute concentrations (n_i) of magnetic impurities. Here we examine how dilute the impurities must be for this to be valid by developing a virial expansion in impurity density. The O(n_i^2) term is determined from results on the 2-impurity Kondo problem by averaging over the RKKY coupling. The non-trivial fixed point of the 2-impurity problem could produce novel singularities in the heat capacity of dilute alloys at O(n_i^2).