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Abstract
The effective s–d spin interaction is derived exactly for the single-impurity Anderson model via a unitary transformation. This unitary transformation was calculated up to infinite order and no restrictions were imposed upon the coefficients of the Hubbard interaction and the hybridization. We also discuss briefly the impact of the obtained result on the magnetic properties of several Kondo compounds. This will shed new light on the understanding of the competition between the Kondo effect and the Ruderman–Kittel–Kasuya–Yosida interaction and reinterpret the Doniach diagram.