Record breaking statistics near second order phase transitions

TL;DR

This study investigates how record-breaking events in order parameter time series can signal proximity to critical points in phase transitions, revealing power law scaling and universality class dependence.

Contribution

It introduces a novel approach of analyzing record statistics as precursors to criticality in both equilibrium and non-equilibrium models.

Findings

Record events peak near critical points.

Power law scaling of record statistics is observed.

Exponents depend on universality class.

Abstract

When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models near their critical points. Specifically, we choose transversely driven Edwards-Wilkinson model for interface depinning in (1+1) dimensions and the Ising model in two dimensions, as paradigmatic and simple examples of non-equilibrium and equilibrium critical behaviors respectively. The total number of record breaking events in the time series of the order parameters of the models show maxima when the system is near criticality. The number of record breaking events and associated quantities, such as the distribution of the waiting time between successive record events, show power law scaling near the critical point. The exponent values are specific to the universality classes of the respective models. Such behaviors near criticality can be used as a precursor to imminent criticality i.e. abrupt and catastrophic changes in the system. Due to the extreme nature of the records, its measurements are relatively free of detection errors and thus provide a clear signal regarding the state of the system in which they are measured.