Mean-field description of a dilute s– d system

Abstract

The Feynman–Kac theorem and Bogolyubov inequality are applied to obtain a lower bound and an upper bound to the free energy of the s– d Hamiltonian with locally smeared interactions between electrons and impurities. The two bounds, which express in terms of the free energy of impurities in a mean field and electrons in a field of barriers and wells localized at the impurity sites, are almost equal if the impurity concentration is sufficiently small or s– d coupling sufficiently weak.