Disorder-aided Early Warning Signals: Predicting Catastrophic Shifts in Athermal Systems

Abstract

The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat becomes particularly acute in low-fluctuation environments, where tipping occurs through saddle-node bifurcation without prior warning in noise dynamics. In this study, we investigate the tipping point dynamics of avalanche catastrophes in low-fluctuation domain, employing model system like the zero temperature random field Ising model and thermally deposited cobalt films. As the system approaches the tipping point, avalanche activity reveals pronounced critical behaviour, including critical slowing down, variance enhancement, and a growing spatial correlation length--hallmarks that may serve as early warning signals of impending collapse. Crucially, we demonstrate that increasing disorder in the system reduces its vulnerability to catastrophic failure. In highly disorder regimes, these early warning signals emerge well before the transition, thereby providing a large margin for anticipation and mitigation. This key finding suggests a protective role of disorder offering a novel perspective on resilience in complex systems. Our results not only deepen the understanding of tipping phenomena in disorder materials but also have broader implications for forecasting regime shift in diverse real-world systems.

Figures (1)

• Figure 1: (a) Regime shift carried by successive avalanches due to a change in the external field with a step size of $\delta H = 0.0005$ and corresponding schematic basin of attraction. (b1-b2) Avalanche distribution for small variable intervals ($\Delta H = 0.1$) at different fields before the line of tipping point ($H_{TP} = -1.41$). As the inflection point approaches, large-scale avalanches appearer accompanied by a change in distribution from multimodal to unimodal (insets). The system shows critical slowing down due to the shrinking basin of attraction proximity to the tipping point. The increase in relaxation time constant (c), spatial correlation length (c), and the variance of the response function (d) at the transition point are indications of the slowing down. The data shown here correspond to the decreasing field, in the step of $\delta H = 0.0005$, applied to $256^3$ system containing disorder strength $\sigma = 2.3$. Here, a regime shift has been presented for up-to-down spin polarization due to an increasing negative field, referred to as the decreasing field. The same phenomenon can be observed for the positive branch of the hysteresis (down to up).