Hidden collective oscillations in a disordered mean-field spin model with non-reciprocal interactions

TL;DR

This paper investigates how separable quenched disorder affects a non-equilibrium mean-field spin model with non-reciprocal interactions, revealing hidden oscillations through specific observables and susceptibilities.

Contribution

It introduces a disorder-dependent observable and generalized susceptibilities to detect oscillations in a disordered non-reciprocal spin model, extending understanding of phase transitions in such systems.

Findings

Separable disorder masks the phase transition in magnetisation signals.

Third-order susceptibilities reveal the onset of oscillations.

Overlap distribution indicates oscillations without explicit disorder knowledge.

Abstract

We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the disordered model, the magnetisation and its time derivative no longer carry the signature of the phase transition to an oscillating state. However, thanks to the separable (Mattis-type) form of the disorder, the presence of oscillations can be revealed by introducing a specific, disorder-dependent observable. We also introduce generalised linear and non-linear susceptibilities associated either with the magnetisation or with its time derivative. While linear susceptibilities show no sign of a phase transition, the third-order susceptibilities present a clear signature of the onset of an oscillating phase. In addition, we show that the overlap distribution also provides evidence for the presence of oscillations, without explicit knowledge of the disorder.