The Green's-function equations describing an electron gas in the presence of a magnetic impurity have been approximated by Nagaoka by means of a truncation procedure that keeps correlations between the spins of the impurity and a conduction electron, but neglects higher correlations. Nagaoka's approximate equations are examined here and reformulated as a one-dimensional nonlinear equation. This equation is solved for temperatures not too close to TK, a characteristic temperature of the system, and shown to have two solutions: a normal solution which exists at all temperatures and a condensed solution valid only below TK. Perturbative corrections to the normal solution are presented.
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Falk et al. (1967) studied this question.
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