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Universal fluctuations in correlated systems

Bramwell1, Christensen, Fortin

  • 1Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom.

Physical Review Letters
|October 6, 2000
PubMed
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Researchers identified a universal probability density function (PDF) for global measures in correlated systems. This finding applies to the 2D XY model

Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Highly correlated systems often exhibit similar statistical properties.
  • The functional form of global measures' probability density functions (PDFs) has been theorized to be universal.

Purpose of the Study:

  • To analytically determine the PDF of the order parameter in the 2D XY model's low-temperature phase.
  • To demonstrate the universality of this PDF across diverse correlated systems.

Main Methods:

  • Analytical derivation of the PDF for the 2D XY model's order parameter.
  • Comparison of the derived PDF with empirical data from various complex systems.

Main Results:

  • The analytical form of the PDF for the 2D XY model's order parameter was identified.

Related Experiment Videos

  • This PDF was shown to accurately describe global quantity fluctuations in equilibrium and nonequilibrium systems.
  • Applicability demonstrated across models including coupled rotors, Ising, percolation, forest fires, sandpiles, avalanches, and granular media.

    • Conclusions:

    • A universal PDF governs global measure fluctuations in a wide range of correlated systems.
    • The identified PDF provides a unifying framework for understanding complex system behavior.
    • This work bridges Gaussian and extremal statistics in the context of correlated systems.