Temporal Griffiths Phases

Vazquez, Federico; Bonachela, Juan Antonio; López, Cristóbal; Muñoz, Miguel Angel
Physical Review Letters 106, 235702 (2011)

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.

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