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Record-breaking statistics near second-order phase transitions.

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Record-breaking events in system dynamics signal critical transitions. Studying these extreme events in models like the Ising model reveals power-law scaling near critical points, offering a precursor to abrupt changes.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Records in time series signify extreme events, surpassing all previous values.
  • Critical points in physical systems are characterized by significant changes in behavior.

Purpose of the Study:

  • To investigate the statistical properties of records in order parameter time series near critical points.
  • To explore the potential of record events as precursors to critical transitions.

Main Methods:

  • Numerical simulations of the (1+1)D transversely driven Edwards-Wilkinson model (nonequilibrium).
  • Numerical simulations of the 2D Ising model (equilibrium).
  • Analysis of record-breaking event frequency and waiting time distributions.

Main Results:

  • Record-breaking events in order parameters peak near critical points.
  • The number of records and waiting times exhibit power-law scaling close to criticality.
  • Scaling exponents are characteristic of the models' universality classes.

Conclusions:

  • Record events serve as sensitive indicators of proximity to critical points.
  • These findings suggest record analysis can predict abrupt system changes.
  • Record measurements are robust against detection errors, providing reliable system state signals.