Q-voter model with independence on signed random graphs: Homogeneous approximations.

Area of Science:

• Statistical Physics
• Network Science
• Sociophysics

Background:

• The q-voter model is a fundamental tool for studying opinion dynamics.
• Signed networks introduce complexity with reinforcing and antagonistic interactions.
• Understanding opinion formation in complex networks is crucial for social and economic modeling.

Purpose of the Study:

• To generalize the q-voter model to signed random graphs.
• To investigate the impact of network sign structure and agent independence on opinion dynamics.
• To analyze the conditions for ferromagnetic and spin-glass-like transitions.

Main Methods:

• Monte Carlo simulations were employed to study the model.
• Mean-field approximation and various pair approximations were used for theoretical analysis.
• The study analyzed quenched disorder in signed networks with varying interaction fractions.

Main Results:

• A ferromagnetic transition was observed, its order depending on model parameters (q, r).
• The transition disappears for large fractions of antagonistic interactions (r).
• Numerical evidence for a spin-glass-like transition was found for large r.

Conclusions:

• The mean-field approximation qualitatively reproduces the phase diagram.
• A refined signed homogeneous pair approximation provides quantitative agreement with simulations for the ferromagnetic transition.
• The study highlights the importance of network structure and interaction types in opinion dynamics.