Majority-vote model on random graphs.

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• The majority-vote model is a fundamental tool for studying opinion dynamics and phase transitions in networks.
• Erdös-Rényi random graphs provide a foundational model for analyzing network structures and their properties.
• Understanding phase transitions in noisy systems is crucial for various scientific disciplines.

Purpose of the Study:

• To investigate the impact of noise on the majority-vote model specifically on Erdös-Rényi random graphs.
• To characterize the order-disorder phase transition within this system.
• To determine how graph connectivity influences the critical noise parameter and critical exponents.

Main Methods:

• Utilized Monte Carlo simulations to model the majority-vote dynamics on random graphs.
• Systematically varied the mean connectivity (z) of the Erdös-Rényi graphs.
• Calculated critical exponents (beta/nu, gamma/nu, 1/nu) at different connectivity values.

Main Results:

• Identified a critical noise parameter (qc) that governs the order-disorder phase transition.
• Found that qc is a monotonically increasing function of the mean connectivity (z).
• Observed that the calculated critical exponents satisfy the hyperscaling relation with an effective dimensionality of one.

Conclusions:

• The connectivity of random graphs significantly influences the stability of ordered states in the majority-vote model.
• The system exhibits critical behavior consistent with universality classes described by hyperscaling relations.
• This research provides quantitative insights into phase transitions in network models with noise.