Stickiness in the order parameter time-series as a signature of criticality

We show that, in continuous phase transitions, the order parameter fluctuations in time, are characterized by a resonant phenomenon, occurring whenever a physical system enters in a critical region. It is realized in the mean waiting time 〈λ〉 of the order parameter time-series, in the immediate neighbourhood of its equilibrium (mean) value. By varying the control parameter within the critical region, 〈λ〉 becomes maximum at the critical point. To illustrate this resonant behaviour, we first use simulated data of the 3D ferromagnetic Ising model. Subsequently, we demonstrate the universality of this phenomenon in experimental voltage drop across the resistor data of a driven resistor–inductor–diode circuit for different driving frequencies. The latter has been recently shown (Potirakis et al., 2017) to act as the order parameter of a continuous transition from normal rectifier phase, in the low frequency regime, to a full-wave conducting, capacitor-like phase at high frequencies. Using a simple phenomenological ansatz for the waiting time distribution within the critical region, we gain some insight to the emergence of the critical resonance, achieving at the same time a semi-quantitative description. •Stickiness properties in the order parameter timeseries are explored.•At the critical point the mean waiting time around order parameter mean value becomes maximum.•The resonant behaviour in the mean waiting time provides a signature for the critical point location.•This resonant behaviour is associated with increased cross-correlations in order parameter time-series.•A possible mechanism for the emergence of these cross-correlations is intermittency.