Temporal disorder does not forbid discontinuous absorbing phase transitions in low dimensional systems

TL;DR

This study investigates the impact of temporal disorder on discontinuous absorbing phase transitions in low-dimensional systems, finding that temporal disorder generally does not prevent such transitions and behaves similarly to pure systems.

Contribution

It demonstrates through three examples that temporal disorder does not inhibit discontinuous phase transitions in two-dimensional systems, contrasting with spatial disorder effects.

Findings

Temporal disorder does not prevent discontinuous transitions.

Transitions exhibit bistability and finite size scaling similar to pure systems.

No temporal Griffiths phases are observed around phase transitions.

Abstract

Distinct works have claimed that spatial (quenched) disorder can suppress the discontinuous absorbing phase transitions. Conversely, the scenario for temporal disorder for discontinuous absorbing phase transitions is unknown. In order to shed some light in this direction, we tackle its effect in three bidimensional examples, presenting undoubtedly discontinuous absorbing phase transitions. Except in one case (to be explained further), the temporal disorder is introduced by allowing the control parameter to be time dependent $p\rightarrow p(t)$ according to a uniform distribution of mean $p_0$ and width $\sigma$, in which at the emergence of the phase transition the system transits between active and absorbing regimes. In contrast to the spatial disorder, numerical results strongly suggest that temporal disorder does not forbid the existence of discontinuous transition. All cases are signed by behaviors similar to their pure (without disorder) counterparts, including bistability around the coexistence point and common finite size scaling behavior with the inverse of the system volume, as recently proposed in Phys. Rev. E. {\bf 92}, 062126 (2015). We also observe that temporal disorder does not induce temporal Griffiths phases around phase transitions, at least for $d=2$.