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Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs.

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Mean-field approximation (MFA) accurately describes Ising-like models on directed graphs with heat-bath dynamics. MFA

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Area of Science:

  • Statistical Mechanics
  • Network Science
  • Computational Physics

Background:

  • Ising-like models are fundamental in statistical mechanics.
  • Understanding nonequilibrium models on complex networks is crucial.
  • Directed regular random graphs offer a tractable network structure.

Purpose of the Study:

  • To investigate the accuracy of mean-field approximation (MFA) for Ising-like models on directed regular random graphs.
  • To compare MFA with Monte Carlo simulations and generating functional analysis.
  • To analyze the impact of different dynamics (heat-bath vs. Metropolis) on model behavior.

Main Methods:

  • Single-site mean-field approximation (MFA).
  • Monte Carlo simulations.
  • Analysis of directed network implementations of Ising, Ising with absorbing states, and majority voter models.

Main Results:

  • MFA accurately reproduces stationary characteristics for models with heat-bath dynamics on these graphs.
  • MFA results align with generating functional analysis for heat-bath dynamics.
  • MFA shows reduced accuracy for models with Metropolis dynamics due to neglected correlations.
  • Heat-bath models exhibit continuous phase transitions, Metropolis models show discontinuous transitions.

Conclusions:

  • MFA provides an exact description for Ising-like models with heat-bath dynamics on directed regular random graphs due to uncorrelated neighbors.
  • The uncorrelated nature of neighbors on these specific graphs is key to MFA's success.
  • Correlations become significant for Metropolis dynamics, limiting MFA's accuracy.
  • Models with heat-bath dynamics belong to the Ising mean-field universality class at the critical point.