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This study explores the q-voter model on multiplex networks, finding that agent independence influences ferromagnetic phase transitions. Network topology and mean degree impact transition details, with good agreement between theory and simulation when mean degree exceeds the q-lobby size.

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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.