Abstract
In the narrow-band limit, the correlation between two localized magnetic moments with spin $S=\frac{1}{2}$ is calculated exactly in the case where both moments are subjected to a direct antiferromagnetic Heisenberg interaction of strength $G$ as well as a ferromagnetic $s\ensuremath{-}d$ interaction of strength $J$ with the conduction electrons. It appears that the correlation exhibits a discontinuity as a function of $\frac{J}{G}$ in the case where the spin clouds, which are built up by the electron gas around the moments, overlap. Another interesting feature is the fact that the two types of interaction are unable to cancel out each other, i.e., a correlation which equals zero does not appear. It also appears that the two moments can never be coupled in a purely antiferromagnetic way unless in the trivial case $J=0$.
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