Temporal disorder in discontinuous non-equilibrium phase transitions: general results

TL;DR

This paper develops a general theory for how temporal disorder affects discontinuous non-equilibrium phase transitions, showing that disorder can turn some first-order transitions into continuous ones and induce Griffiths phases.

Contribution

It provides a unified framework for understanding the impact of temporal disorder on discontinuous phase transitions, including stability analysis and universality classes.

Findings

Temporal disorder does not destroy discontinuous transitions in the quadratic contact process.

Strong disorder can convert first-order transitions into continuous ones with infinite-noise criticality.

Rare temporal fluctuations induce a temporal Griffiths inactive phase with large decay times.

Abstract

We develop a general theory for discontinuous non-equilibrium phase transitions into an absorbing state in the presence of temporal disorder. We focus in two paradigmatic models for discontinuous transitions: the quadratic contact process (in which activation is only spread when two nearest- neighbor sites are both active) and the contact process with long-range interactions. Using simple stability arguments (supported by Monte Carlo simulations), we show that temporal disorder does not destroy the discontinuous transition in the former model. For the latter one, the first-order transition is turned into a continuous one only in the strong-disorder limit, with critical behavior belonging to the infinite-noise universality class of the contact process model. Finally, we have found that rare temporal fluctuations dramatically changes the behavior of metastable phase turning it into a temporal Griffiths inactive phase characterized by an exponentially large decay time.