Pair approximation for the q-voter model with independence on multiplex networks

Area of Science:

• Statistical Physics
• Complex Systems
• Network Science

Background:

• The q-voter model is a fundamental tool for studying opinion dynamics in social systems.
• Multiplex networks, with interconnected layers, offer a more realistic representation of complex social structures.
• Understanding how social influence propagates across different network layers is crucial for predicting collective behavior.

Purpose of the Study:

• To investigate the q-voter model with independence on multiplex networks.
• To analyze the impact of different spin update rules (LOCAL&AND, GLOBAL&AND) on opinion formation.
• To compare theoretical predictions with simulation results for phase transitions.

Main Methods:

• Development of a homogeneous pair approximation for spin models on multiplex networks.
• Conducting Monte Carlo simulations of the q-voter model with independence.
• Analyzing ferromagnetic phase transitions, including order, critical points, and exponents.

Main Results:

• Ferromagnetic phase transitions occur as agent independence changes, with the order (first- or second-order) depending on the lobby size q.
• The homogeneous pair approximation accurately predicts transition details when the mean degree of nodes is significantly larger than q.
• Agreement between theory and simulations is quantitative for homogeneous and weakly heterogeneous networks, but qualitative for strongly heterogeneous scale-free networks.

Conclusions:

• Agent independence is a key factor driving phase transitions in the q-voter model on multiplex networks.
• The homogeneous pair approximation provides a reliable theoretical framework for understanding opinion dynamics in such systems under specific conditions.
• Network topology, particularly mean degree and heterogeneity, critically influences the accuracy of theoretical predictions and the nature of opinion transitions.