Formation of bound states in the Kondo effect

The statistical sum of a metal having paramagnetic impurities with spin S = 1/2 is written by means of a functional integral whose form corresponds to the Nagaoka proposition concerning the formation of bound states between electrons and an impurity in the system. The method of steepest descent is used to calculate the first two terms in the expansion of this integral; the derived expressions coincide with the results of Abrikosov. However, the estimation of the subsequent terms of the expansion shows that, contrary to the assumption made by Abrikosov, they are not small in comparison with the preceding terms throughout the entire temperature range T≥ 0−, T ∼Tk (Tk is the Kondo temperature).

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