Nature of the Griffiths phase.

Arguments are given that, for random spin systems, the density of states \ensuremath{\rho}(\ensuremath{\mu}) of the inverse of the susceptibility matrix vanishes as \ensuremath{\rho}(\ensuremath{\mu})\ensuremath{\sim}exp(-A/\ensuremath{\mu}), for \ensuremath{\mu}\ensuremath{\rightarrow}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\ensuremath{\rightarrow}\ensuremath{\infty}, the spin autocorrelation function C(t) is found to have the ``stretched-exponential'' form, lnC(t)\ensuremath{\sim}-(At${)}^{1/2}$, in the Griffiths phase.