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Exact solution to the random sequential dynamics of a message passing algorithm.

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Summary
This summary is machine-generated.

We analyzed random sequential dynamics for Ising models. The de Almedia-Thouless criterion determines global convergence for these complex systems.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Computational neuroscience

Background:

  • Ising models are fundamental to understanding magnetism and neural networks.
  • Random interactions introduce complexity, requiring advanced analytical methods.
  • Message passing algorithms are crucial for large-scale simulations.

Purpose of the Study:

  • To analyze the random sequential dynamics of message passing algorithms in Ising models.
  • To derive exact results for correlation functions and convergence speed.
  • To investigate the role of the de Almedia-Thouless criterion in dynamics.

Main Methods:

  • Analysis of random sequential dynamics in the large system limit.
  • Derivation of exact results for two-time correlation functions.
  • Application of the de Almedia-Thouless stability criterion.

Main Results:

  • Exact results for two-time correlation functions were obtained.
  • The speed of convergence for the dynamics was determined.
  • The de Almedia-Thouless criterion was shown to be necessary and sufficient for global convergence.

Conclusions:

  • The de Almedia-Thouless criterion governs the global convergence of random sequential dynamics in Ising models.
  • This finding bridges static stability and dynamic behavior in complex systems.
  • Provides a theoretical framework for understanding convergence in large, random systems.