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Arkadiusz Jędrzejewski1, Katarzyna Sznajd-Weron1

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We compared annealed and quenched randomness in the q-voter model. Quenched randomness promotes continuous phase transitions, while annealed randomness favors discontinuous ones, offering distinct macroscopic behaviors.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Sociophysics

Background:

  • The nonlinear q-voter model is a key tool for studying opinion dynamics.
  • Understanding the role of randomness is crucial for modeling real-world social behaviors.
  • Distinguishing between annealed and quenched randomness impacts macroscopic outcomes.

Purpose of the Study:

  • To compare the macroscopic effects of annealed versus quenched randomness in the nonlinear q-voter model.
  • To derive and analyze the phase diagrams for both models.
  • To investigate the nature of phase transitions under different randomness conditions.

Main Methods:

  • Mean-field description of the nonlinear q-voter models.
  • Stability analysis using linearization techniques from dynamical system theory.
  • Monte Carlo simulations on a complete graph for validation.

Main Results:

  • Both models yield the same average microscopic opinion changes but differ macroscopically.
  • Quenched randomness favors continuous phase transitions; annealed randomness favors discontinuous ones.
  • The quenched model exhibits unique phase transition combinations and symmetry breaking not seen in the annealed model.

Conclusions:

  • The type of randomness significantly influences the macroscopic behavior and phase transitions in opinion dynamics models.
  • Dynamical system theory provides exact phase diagrams for these models.
  • Quenched randomness offers richer phenomena, including novel symmetry breaking patterns.