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.