  An Ising spin system under the critical temperature driven by a dichotomous
Markov noise (magnetic field) with a finite correlation time is studied both
numerically and theoretically. The order parameter exhibits a transition
between two kinds of qualitatively different dynamics, symmetry-restoring and
symmetry-breaking motions, as the noise intensity is changed.
  There exist regions called channels where the order parameter stays for a
long time slightly above its critical noise intensity. Developing a
phenomenological analysis of the dynamics, we investigate the distribution of
the passage time through the channels and the power spectrum of the order
parameter evolution. The results based on the phenomenological analysis turn
out to be in quite good agreement with those of the numerical simulation.
