  Inspired by the models of A. Rebei and G. J. Parker and A. Rebei et. al., we
study a physical model which describes the behaviour of magnetic moments in a
ferromagnet. The magnetic moments are associated to 3d electrons which interact
with conduction band electrons and with phonons. We study each interaction
separately and then collect the results assuming that the electron-phonon
interaction can be neglected. For the case of the spin-phonon interaction, we
study the derivation of the equations of motion for the classical spin vector
and find that the correct behaviour, as given by the Brown equation for the
spin vector and the Bloch equation, using the results obtained by D. A. Garanin
for the average over fluctuations of the spin vector, can be obtained in the
high temperature limit. At finite temperatures we show that the Markovian
approximation for the fluctuations is not correct for time scales below some
thermal correlation time $\tau_{Th}$. For the case of electrons we workout a
perturbative expansion of the Feynman-Vernon functional. We find the expression
for the random field correlation function. The composite model (as well as the
individual models) is shown to satisfy a fluctuation-dissipation theorem for
all temperature regimes if the behaviour of the coupling constants of the
phonon-spin interaction remains unchanged with the temperature. The equations
of motion are derived.
