Temporal Griffiths Phases

TL;DR

This paper introduces Temporal Griffiths phases (TGPs), a new concept describing how temporal disorder causes extended regions of scale invariance and divergence in susceptibility in systems with absorbing states, especially in dimensions two and higher.

Contribution

It extends the concept of Griffiths phases to temporal disorder, revealing the existence of TGPs with power-law spatial scaling and divergence of susceptibility, highlighting the role of time in disorder effects.

Findings

TGPs exist for dimensions d ≥ 2.

TGPs exhibit power-law spatial scaling.

Susceptibility diverges in TGPs.

Abstract

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 $d \geq 2$ there are 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.