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Dynamic message-passing approach for kinetic spin models with reversible dynamics.

Gino Del Ferraro1, Erik Aurell1,2,3

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This study introduces a novel method for approximating dynamic cavity equations in reversible dynamics. The technique accurately reconstructs transient and equilibrium dynamics for the kinetic Ising model on random graphs.

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Area of Science:

  • Statistical physics
  • Computational physics

Background:

  • Dynamic cavity methods are crucial for analyzing complex systems.
  • Approximating solutions for reversible dynamics on treelike structures remains challenging.

Purpose of the Study:

  • To present a new method for approximately closing dynamic cavity equations.
  • To validate the method for synchronous reversible dynamics on locally treelike topologies.

Main Methods:

  • Utilizes a graph expansion to remove loops in normalization steps.
  • Employs an assumption of local temporal dependencies in auxiliary probability distributions.
  • Projects probability distributions onto n-step Markov processes for closure.

Main Results:

  • The method is detailed for ordinary Markov processes (n=1) and outlined for higher-order approximations (n>1).
  • Numerical validations demonstrate accurate reconstruction of transient and equilibrium dynamics.
  • The kinetic Ising model on a random graph with arbitrary connectivity symmetry was successfully analyzed.

Conclusions:

  • The presented method offers an effective approach for approximating dynamic cavity equations.
  • This technique is applicable to analyzing the dynamics of complex systems, including the kinetic Ising model.
  • The findings pave the way for more efficient simulations of reversible dynamics.