II. Locally enhanced spin fluctuations viewed within the Wilson theory. Comparison with the Kondo problem

Abstract

We give here the details of a brief report given elsewhere and based on the study developed in the previous paper (I). We begin by citing the analogy between the behavior of a ferromagnet above its Curie temperature and an itinerant strongly interacting set of fermions at 0 K. We show that this analogy holds beyond the well-known mean-field results. We then develop a calculation similar to the Wilson theory of phase transitions, using a Lagrangian established in paper I for locally interacting fermions and shown to be comparable to the Wilson Lagrangian. We find that the renormalized local enhancement on a nearly magnetic impurity has the same form as in mean-field theory but with a renormalized local interaction actually weaker than the Hartree-Fock one. We conclude that the stable fixed point in that theory should correspond to a vanishing local interaction between the fermions. This last result is compared with the stable fixed pointJ=−∞ of the Kondo problem. In the present case the theory of local paramagnons appears to actually be a weak coupling theory. A contrast between the problems of local spin fluctuations and uniform ones is also pointed out.