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, $t^{\mathrm{-}x}$, with the exponent x in general being nonuniversal. For systems with quenched random-field disorder the decay is slower still, as exp[-k(lnt${)}^{\left(d\mathrm{-}2\right)/\left(d\mathrm{-}1\right)}$], 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.

• Received 30 October 1986

DOI:https://doi.org/10.1103/PhysRevB.35.6841