Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs
Adam Lipowski1, António L Ferreira2, Dorota Lipowska3
1Faculty of Physics, Adam Mickiewicz University in Poznań, 61-614 Poznań, Poland.
Entropy (Basel, Switzerland)
|December 23, 2023
Summary
Mean-field approximation (MFA) accurately describes Ising-like models on directed graphs with heat-bath dynamics. MFA
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.
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