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Mean-field approximation and phase transitions in an Ising-voter model on directed regular random graphs.
Adam Lipowski1, António Luis Ferreira2, Dorota Lipowska3
1Adam Mickiewicz University, Faculty of Physics and Astronomy, Poznań 61-614, Poland.
Physical Review. E
|March 19, 2025
Summary
Voter agents don't change Ising models, but antivoter agents weaken magnetic ordering. Mean-field theory accurately describes Ising models with heat-bath dynamics, but not Metropolis dynamics, especially with antivoters.
Area of Science:
- Statistical Mechanics
- Complex Systems
Background:
- Ising-like systems on directed graphs typically exhibit vanishing neighbor correlations, allowing for mean-field approximations.
- Heterogeneous agent-based models introduce complexities not fully captured by standard mean-field approaches.
Purpose of the Study:
- To investigate the impact of heterogeneous voter and antivoter dynamics on Ising-like systems.
- To determine the validity of mean-field approximations under these modified dynamics and different update rules.
Main Methods:
- Analysis of modified Ising models with fractions of agents using voter or antivoter dynamics.
- Comparison of heat-bath and Metropolis dynamics for spin updates.
- Simulations on annealed networks and calculation of the Binder cumulant.
Main Results:
- Voter dynamics do not alter the system's behavior, which remains akin to a pure Ising model.
- Antivoter dynamics introduce noise, weakening ferromagnetic ordering and deviating from mean-field predictions with Metropolis dynamics.
- Heat-bath dynamics align with mean-field approximations, while Metropolis dynamics require heterogeneous models for agreement, especially with antivoters.
Conclusions:
- Heat-bath dynamics in heterogeneous Ising models with antivoters fall within the Ising mean-field universality class.
- Metropolis dynamics likely result in a discontinuous phase transition, particularly with fewer antivoter agents.
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