On the specific heat for a dilute magnetic alloy

Abstract

Here we report a calculation of the specific heat of a dilute magnetic alloy, which can be described by the Anderson model. The calcul&tion is an extension of a previous calculation of the magnetic susceptibility which was described in a paper called I (l), where also further references are given. In that paper it was shown that the two-body Coulomb interaction U between electrons localized at an impurity formally can be replaced by the interaction with fluctuating external fields. The partition function for the system was shown to be given a s a Gaussian average of the corresponding partition function for conduction electrons in these external fields. In the case of static external fields it was shown that the calculated magnetic susceptibility agreed with perturbation theory. In the case of strong Coulomb interaction the system showed localized moments with a Curie-law susceptibility, and in the case of weak interaction the system had no moments and the susceptibility approached a Pauli-enhanced temperature independent susceptibility. The two situations were related to the existence o r non-existence of an additional minimum in the effective free energy.Here we use the same technique in an attempt to evaluate the specific heat of the system. However, this is a more difficult task since it turns out that the value of the specific heat depends on how the additional minimum in the free energy changes with temperature. In paper I the partition function was written as an integral over the external field in the static approximation

Functional integral methods in the theory of the Anderson model

“…A detailed discussion of the s-d model and of the Kondo effect is outside the scope of this review : while referring the reader unfamiliar with them to the existing literature (Kondo 1969, Fischer 1971, Anderson and Yuval 1969, 1972, we recall only a few points.…”

“…Section 6 is devoted to the approximation schemes (RPA', quartic and harmonic approximations) which aim at improving over the static approximation. Section 7 deals with a problem of central relevance for the Anderson model, that is the connections with the s-d model and therefore with the Kondo effect (Kondo 1969). In § 8 we have collected a few miscellaneous topics, namely the studies (a very few indeed) of the two and many impurity problems and the extensions of the methods to dilute superconducting alloys.…”