Random one-body approximation to the Hubbard model: magnetic interactions

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Abstract
Within the binary, self-consistent static approximation to the Hubbard-model, local moments are created out of itinerant electrons. The magnetic Ising-type interactions of these local moments are calculated and explicit results are obtained. Relaxing the static character of the approximation transforms the interactions to Heisenberg type and renormalises their size. Renormalisation is necessary in order to satisfy certain sum rules. The authors' results are in good agreement with exact many-body results.