  The time-dependent behavior of the Heisenberg model in contact with a phonon
heat bath and in an external time-dependent magnetic field is studied by means
of a path integral approach. The action of the phonon heat bath is taken into
account up to the second order in the coupling to the heath bath. It is shown
that there is a minimal value of the magnetic field below which the average
magnetization of the system does not relax to equilibrium when the external
magnetic field is flipped. This result is in qualitative agreement with the
mean field results obtained within $\phi^{4}$-theory.

Statistical Mechanics