Temporal disorder in up-down symmetric systems

TL;DR

This paper investigates how temporal disorder affects up-down symmetric systems, revealing the emergence of Temporal Griffiths Phases characterized by algebraic scaling and diverging susceptibility, with implications for ecological models.

Contribution

It demonstrates the robustness and ubiquity of Temporal Griffiths Phases in systems with temporal disorder, extending understanding of phase transitions under fluctuating global conditions.

Findings

Temporal Griffiths Phases occur in both Ising and voter classes under temporal disorder.

TGPs exhibit algebraic mean first-passage times and diverging susceptibility.

Temporal disorder's effects are robust and relevant to ecological systems.

Abstract

The effect of temporal disorder on systems with up-down Z2 symmetry is studied. In particular, we analyze two well-known families of phase transitions: the Ising and the generalized voter universality classes, and scrutinize the consequences of placing them under fluctuating global conditions. We observe that variability of the control parameter induces in both classes "Temporal Griffiths Phases" (TGP). These recently-uncovered phases are analogous to standard Griffiths Phases appearing in systems with quenched spatial disorder, but where the roles of space and time are exchanged. TGPs are characterized by broad regions in parameter space in which (i) mean first-passage times scale algebraically with system size, and (ii) the system response (e.g. susceptibility) diverges. Our results confirm that TGPs are quite robust and ubiquitous in the presence of temporal disorder. Possible applications of our results to examples in ecology are discussed.