Temporal Griffiths Phases

Abstract

Disorder is an unavoidable ingredient of real systems. Spatial disorder generates {\it Griffiths phases} (GPs) which, in analogy to critical points, are characterized by a slow relaxation of the order parameter and divergences of quantities such as the susceptibility. However, these singularities appear in an extended region of the parameter space and not just at a (critical) point, i.e. there is {\it generic scale invariance}. Here, we study the effects of temporal disorder, focusing on systems with absorbing states. We show that for dimensions $d \geq 2$ there are {\it Temporal Griffiths phases (TGPs)} characterized by generic power-law spatial scaling and generic divergences of the susceptibility. TGPs turn out to be a counterpart of GPs, but with space and time playing reversed roles. TGPs constitute a unifying concept, shedding light on the non-trivial effects of temporal disorder.