Temporal Griffiths phases

Vazquez, Federico and Bonachela, Juan A. and López, Cristóbal and Muñoz, Miguel A. (2011) Temporal Griffiths phases. Physical Review Letters, 106 (23). 235702. ISSN 1079-7114 (https://doi.org/10.1103/PhysRevLett.106.235702)

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Disorder is an unavoidable ingredient of real systems. Spatial disorder generates 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 generic scale invariance. Here, we study the effects of temporal disorder, focusing on systems with absorbing states. We show that for dimensions d2 there are Temporal Griffiths phases (TGPs) characterized by generic power-law scaling of some magnitudes 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 nontrivial effects of temporal disorder.