Low-Frequency Relaxation in Ising Spin-Glasses

For $d$-dimensional short-range Ising spin-glasses with local spin-flip dynamics, the correlation function $〈s_i\mathrm{}\left(0\right)\mathrm{}{s}_i\mathrm{}\left(t\right)\mathrm{}〉$ is argued to be bounded below by a function of the form $\exp [-c{\left(\ln t\right)}^{\frac{d}{\mathrm{}(d-1\mathrm{})\mathrm{}}}]$ in a temperature range above the spin-glass transition. The slow relaxation of large isolated clusters of unfrustrated spins is responsible for this bound. We suggest that this is the signature for an intermediate Griffiths phase between the spin-glass and the paramagnetic phases.