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 nonexponential decay of temporal spin autocorrelations. For the two-dimensional pure Ising model the long-time decay is a stretched exponential, exp(- {}t/{τ} ), where t is time and {τ} a correlation time. For systems with quenched random-exchange disorder the spatially averaged correlation decays as a power of time, t^-x, with the exponent x in general being nonuniversal. For systems with quenched random-field disorder the decay is slower still, as exp[-k(lnt)^(d-2)/(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.