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  11. Correlation Thresholds In The Steady States Of Particle Systems And Spin Glasses

Correlation thresholds in the steady states of particle systems and spin glasses

Jacob Calvert1,2, Dana Randall2,3

  • 1Georgia Institute of Technology, Institute for Data Engineering and Science, Atlanta, Georgia 30332, USA.

Physical Review. E
|January 21, 2026

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View abstract on PubMed

Summary
This summary is machine-generated.

Global steady-state distributions in complex systems often mimic the Boltzmann distribution. We found a critical correlation threshold linked to system dynamics, explaining approximation quality.

Area of Science:

  • Statistical Mechanics
  • Complex Systems Theory
  • Dynamical Systems

Background:

  • Many equilibrium and nonequilibrium systems exhibit steady-state distributions that approximate the Boltzmann distribution.
  • A key factor in this approximation's accuracy is the correlation between the effective potential and exit rates.

Purpose of the Study:

  • To demonstrate and explain the Boltzmann distribution analog in complex systems.
  • To investigate the correlation between effective potential and exit rates.
  • To identify and explain thresholds in this correlation.

Main Methods:

  • Analysis of a one-dimensional particle system.
  • Study of random dynamics in the Sherrington-Kirkpatrick spin glass model.
  • Explicit estimation of the correlation between effective potential and logarithm of exit rates.

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Main Results:

  • The correlation between effective potential and exit rates significantly influences the Boltzmann distribution approximation.
  • Both systems studied showed distinct correlation behaviors above and below specific dynamic parameter thresholds.
  • These thresholds correspond to transitions in the relationship between local and global effective potential components.

Conclusions:

  • The Boltzmann distribution analog in complex systems is robust but sensitive to dynamic parameter changes.
  • Understanding the correlation thresholds provides insight into the underlying physics of these systems.
  • The findings offer a method to assess and improve approximations of steady-state distributions.