  We consider the ferromagnetic Ising model with Glauber spin flip dynamics in
one dimension. The external magnetic field vanishes and the couplings are
i.i.d. random variables. If their distribution has compact support, the
disorder averaged spin auto-correlation function has an exponential decay in
time. We prove that, if the couplings are unbounded, the decay switches to
either a power law or a stretched exponential, in general.
