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Rényi information flow in the Ising model with single-spin dynamics.

Zehui Deng1, Jinshan Wu2, Wenan Guo3

  • 1Physics Department, Beijing Normal University, Beijing 100875, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
PubMed
Summary

We derived information flow measures for the 2D kinetic Ising model. These measures, including Rényi transfer entropy, peak in the disordered phase, revealing insights into complex system dynamics.

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Computational Physics

Background:

  • The Ising model is a fundamental model in statistical mechanics for understanding magnetism and phase transitions.
  • Quantifying information flow is crucial for analyzing complex systems and emergent behaviors.

Purpose of the Study:

  • To derive and calculate information-theoretic quantities, specifically n-index Rényi mutual information and transfer entropies, for the 2D kinetic Ising model.
  • To investigate the behavior of these information flow measures, particularly their peak locations, in relation to the model's phases.

Main Methods:

  • Derivation of transfer entropies as functions of ensemble averages and spin-flip probabilities.
  • Application of cluster Monte Carlo algorithms (Wolff algorithm) with differing dynamics (Metropolis, Glauber) for simulations.
  • Estimation of information flow using computed transfer entropies.

Main Results:

  • The study successfully derived analytical expressions for information flow measures in the thermodynamic limit.
  • Monte Carlo simulations revealed that both global and pairwise Rényi transfer entropies exhibit peak values within the disorder phase of the Ising model.
  • The findings demonstrate the applicability of cluster Monte Carlo algorithms for estimating transfer entropies.

Conclusions:

  • Information flow, quantified by Rényi transfer entropy, is a sensitive indicator of phase transitions in the 2D kinetic Ising model.
  • The peak in information flow within the disorder phase suggests a high degree of dynamic activity and information exchange in this regime.
  • The developed methods provide a framework for analyzing information dynamics in other complex systems.