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.