Equilibrium behavior in a nonequilibrium system: Ising-doped voter model on complete graph.
Adam Lipowski1, Dorota Lipowska2
1Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.
Physical Review. E
|March 16, 2022
Summary
This study introduces a mixed opinion formation model combining Ising and voter agents. Even with voter agents, the system exhibits Ising-like ferromagnetic ordering and magnetization behavior.
Area of Science:
- Statistical mechanics
- Complex systems
- Social dynamics
Background:
- The Ising model is a fundamental equilibrium system.
- The voter model is a key nonequilibrium opinion dynamics model.
- Understanding mixed systems is crucial for realistic modeling.
Purpose of the Study:
- To investigate an opinion formation model blending Ising and voter agents.
- To analyze the impact of mixing equilibrium and nonequilibrium agents.
- To determine if ferromagnetic ordering persists in mixed systems.
Main Methods:
- Developing a hybrid model with Ising (p) and voter (1-p) agents.
- Analyzing the average magnetization in the stationary state.
- Conducting numerical simulations on complete and random graphs.
Main Results:
- Average magnetization follows the Ising model equation for any p>0 on a complete graph.
- Magnetization variance and susceptibility increase as p decreases.
- A small fraction of Ising agents induces ferromagnetic ordering on random graphs.
Conclusions:
- The mixed model retains key Ising model properties despite violating detailed balance.
- The concentration of Ising agents significantly impacts system dynamics and ordering.
- This hybrid approach offers insights into emergent collective behavior.
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