  We investigate numerically and analytically the heating process in ergodic
clusters of interacting spins 1/2 subjected to periodic pulses of external
magnetic field. Our findings indicate that there is a threshold for the pulse
strength below which the heating is suppressed. This threshold decreases with
the increase of the cluster size, approaching zero in the thermodynamic limit;
yet it should be observable in clusters with fairly large Hilbert spaces. We
obtain the above threshold quantitatively as a condition for the breakdown of
the golden rule in the second-order perturbation theory. It is caused by the
phenomenon of dynamic localization.
