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Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents
André L M Vilela1,2, Bernardo J Zubillaga2, Chao Wang3,4
1Física de Materiais, Universidade de Pernambuco, 50720-001, Recife, Pernambuco, Brazil.
Scientific Reports
|May 20, 2020
Summary
This study explores opinion dynamics using a three-state majority-vote model on complex networks. Researchers found critical exponents sum to unity, a universal property across different network types and dimensions.
Area of Science:
- Statistical Physics
- Complex Networks
- Opinion Dynamics
Background:
- The three-state majority-vote model simulates how opinions spread in a population.
- Understanding opinion dynamics is crucial for social and information network analysis.
Purpose of the Study:
- Investigate the three-state majority-vote model on scale-free and regular networks.
- Determine critical exponents and phase diagrams for opinion dynamics.
- Explore universal scaling properties of critical exponents.
Main Methods:
- Utilized finite-size scaling analysis to determine critical exponents.
- Employed Monte Carlo simulations to calculate critical noise parameters.
- Constructed preferential attachment networks with a specified degree distribution.
Main Results:
- Calculated critical exponents for magnetization and susceptibility.
- Determined the critical noise parameter (q_c) as a function of the growth parameter (z) for scale-free networks.
- Established a phase diagram for the opinion dynamics model.
Conclusions:
- Demonstrated that critical exponents sum to unity under volumetric scaling, irrespective of network dimensionality.
- Validated this universality by analyzing models on cubic lattice networks.
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