Nature of the Griffiths phase

Arguments are given that, for random spin systems, the density of states {ρ}({μ}) of the inverse of the susceptibility matrix vanishes as {ρ}({μ}){~}exp(-A/{μ}), for {μ}{→}0, throughout the ``Griffiths phase.'' The amplitude A vanishes at the onset of magnetic long-range order, and diverges at the transition between ``Griffiths'' and ``paramagnetic'' phases. For an O(m) spin system, with m{→}{∞}, the spin autocorrelation function C(t) is found to have the ``stretched-exponential'' form, lnC(t){~}-(At)1/2, in the Griffiths phase.