Dynamics of droplet fluctuations in pure and random Ising systems.

Long-lived droplet fluctuations can dominate the long-time equilibrium dynamics of long-range ordered Ising systems, yielding non-exponential decay of temporal spin autocorrelations. For the two-dimensional pure Ising model the long-time decay is a stretched exponential, exp(-sqrt (t/tau)), where t is time and tau a correlation time. For systems with quenched random- exchange disorder the spatially averaged correlation decays as a power of time, t sup (-x), with the exponent x in general being nonuniversal. For systems with quenched random-field disorder the decay is slower still, as exp[-k(ln t)/sup(d-2)/sup (d-1)], where k is a nonuniversal number and d is the dimensionality of the system. The low-frequency noise from this slow dynamics may be experimentally detectable, as is the analogous noise in spin glass ordered phases.