FROM THE HUBBARD-MODEL TO CLASSICAL SPIN-FLUCTUATION THEORY

In this paper we develop a microscopic foundation for the Murata-Donia ch model of spin fluctuations which has been widely used in connection with band-structure calculations. The main result of the paper is the formulation of the partition function of an itinerant system as a fun ctional integral over magnetization modes, and an explicit formula for the energy functional appearing in the exponent of the Boltzmann fact or. Such a derivation is made since former theoretical investigations focus on the interaction part of the partition function Z/Z0, whereas the Murata-Doniach model is formulated in terms of a functional integr al for the complete partition function Z. We start with an approximate description of magnetic excitations of noninteracting fermions within collective modes, and derive a bosonlike partition function for these magnetization modes. This is combined with the well-known result for the interaction part of the partition function in the Hubbard model ob tained by functional-integral theory. The leading term of the energy f unctional appearing in the exponent of the partition function agrees w ith that of the Ginzburg-Landau expansion for the energy of a classica l magnetization field. In the course of the transformation to a bosonl ike system we predict that the cutoff wave vector q(c) which must be i ntroduced in the classical model is temperature dependent with q(c) is similar to T1/3. It is shown that the frequencies of the collective m odes are reduced by the Stoner enhancement factor compared with the on e-particle excitation energies of Stoner theory.