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Summary
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The degree-weighted majority vote (DWMV) model exhibits distinct phase transition behaviors on Erdős-Rényi networks (ERNs) and scale-free networks (SFNs). Critical exponents depend on network structure and the influence parameter α, particularly for scale-free networks with low degree exponents.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • The degree-weighted majority vote (DWMV) model is a framework for studying opinion dynamics and phase transitions in networks.
  • Understanding how network topology influences collective behavior is crucial in complex systems.
  • Erdős-Rényi networks (ERNs) and scale-free networks (SFNs) represent distinct network structures with different degree distributions.

Purpose of the Study:

  • To investigate the phase transition properties of the DWMV model on ERNs and SFNs.
  • To analyze the impact of the weight parameter α on the model's behavior across different network types.
  • To determine the universality class and critical exponents of the DWMV model under varying network conditions.

Main Methods:

  • Monte Carlo simulations were employed to model the DWMV dynamics.
  • Finite-size scaling analysis was used to identify critical points and exponents.
  • The study systematically varied the weight parameter α and the degree exponent λ of SFNs.

Main Results:

  • The DWMV model on ERNs and SFNs (λ>5) consistently belongs to the mean-field Ising universality class for all α.
  • On SFNs with 3<λ<5, the Ising universality class is observed only for α=0; for α>0, critical exponents change continuously with α.
  • On SFNs with λ<3, a continuous transition occurs only at α=0, with significant deviations in critical exponents; for α>0, the system remains in the disordered phase.

Conclusions:

  • Network topology, specifically degree distribution, significantly alters phase transition dynamics in the DWMV model.
  • The influence parameter α plays a critical role in determining the model's universality class and critical behavior, especially on heterogeneous networks.
  • The findings highlight the importance of considering network heterogeneity and interaction weights when analyzing collective phenomena in complex systems.