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Phase Transitions of the Majority-Vote Model with Inertia on Directed Erdös-Rényi Networks
Talia Costa Rodrigues1, David Santana Alencar1, Tayroni Alencar Alves1
1Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, Teresina 64049-550, PI, Brazil.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
The majority vote model with inertia exhibits complex phase transitions on directed Erdös-Rényi networks. The inertia parameter significantly alters the transition type, from continuous to first-order, or eliminating it entirely.
Area of Science:
- Statistical physics
- Complex networks
- Computational modeling
Background:
- The majority vote model is a fundamental tool for studying opinion dynamics.
- Incorporating inertia into agent-based models can reveal novel behaviors.
- Directed Erdös-Rényi networks offer a complex topology for network simulations.
Purpose of the Study:
- To investigate the phase transition of the majority vote model with inertia.
- To analyze the impact of the inertia parameter on network opinion dynamics.
- To compare model behavior on directed Erdös-Rényi networks with previous findings on regular networks.
Main Methods:
- Extensive Monte Carlo simulations were employed.
- The study focused on directed Erdös-Rényi networks with an average connectivity of 20.
- Key metrics analyzed included relaxation time, Binder cumulant, and susceptibility.
Main Results:
- The phase transition strongly depends on the inertia parameter.
- Continuous phase transitions occur for inertia between 0 and 0.1.
- First-order transitions are observed for inertia between 0.2 and 0.5, with no transition at higher values.
Conclusions:
- The inertia parameter introduces rich and varied phase transition behaviors.
- Model dynamics are significantly altered by inertia on complex network structures.
- Results differ substantially from those on regular networks, highlighting topological effects.
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