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Published on: May 10, 2012
Domain motion in the voter model with noise
Nazareno G F Medeiros1, Ana T C Silva, F G Brady Moreira
1Departamento de Física, Universidade Estadual de Feira de Santana 44031-460, Feira de Santana, Bahia, Brazil. ngfm@uefs.br
Summary
Adding noise to the voter model on one-dimensional chains slows consensus. Increased noise parameter q lengthens the time to reach complete ordering, affecting domain size and magnetization.
Area of Science:
- Statistical mechanics
- Complex systems
Background:
- The voter model is a fundamental tool for studying opinion dynamics and consensus formation in social and biological systems.
- Understanding the impact of external factors like noise is crucial for realistic modeling.
Purpose of the Study:
- To investigate the effect of noise on consensus-reaching dynamics in the one-dimensional voter model.
- To quantify the relationship between noise parameter and system ordering time, domain size, and magnetization.
Main Methods:
- Monte Carlo simulations were employed to model the voter model with noise.
- Finite-size scaling techniques were utilized to analyze the simulation data.
Main Results:
- The system's evolution towards consensus is significantly altered by the introduction of noise.
- The time required for complete ordering increases with the noise parameter (q).
- Average domain size scales as ξ ∝ q^(-1/2), and magnetization scales as m ∝ N^(-1/2).
Conclusions:
- Noise plays a critical role in modulating consensus dynamics in the one-dimensional voter model.
- The observed scaling relationships provide quantitative insights into how noise affects system ordering.
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