Contact process with temporal disorder

TL;DR

This paper studies how temporal disorder affects the phase transition in the contact process, revealing an exotic infinite-noise critical point characterized by diverging noise and logarithmic decay of key quantities.

Contribution

It introduces the concept of infinite-noise criticality in the contact process due to temporal disorder, combining theoretical and simulation methods to uncover new critical behavior.

Findings

Temporal disorder induces an infinite-noise critical point.

At criticality, noise amplitude diverges over time.

Density and survival probability decay logarithmically.

Abstract

We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.