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This study explores opinion dynamics using the Biswas-Chatterjee-Sen (BChS) model on complex networks. Researchers observed second-order phase transitions and computed critical exponents, finding connectivity-independent behavior.

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Biswas–Chatterjee–Sen modelfinite-size-scaling hypothesisopinion dynamics systemssecond-order phase transitionsuniversality class

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Area of Science:

  • Statistical Physics
  • Complex Networks
  • Computational Social Science

Background:

  • Opinion dynamics models are crucial for understanding social behavior and information diffusion.
  • The Biswas-Chatterjee-Sen (BChS) model offers a discrete framework for simulating opinion formation.
  • Barabási-Albert networks (BANs) represent scale-free networks with heterogeneous connectivity.

Purpose of the Study:

  • To investigate the discrete Biswas-Chatterjee-Sen (BChS) opinion dynamics model on Barabási-Albert networks (BANs).
  • To analyze the impact of noise and network structure on phase transitions and critical exponents.
  • To compare the model's behavior across different network topologies, including directed and random graphs.

Main Methods:

  • Extensive computer simulations utilizing Monte Carlo algorithms.
  • Application of the finite-size scaling hypothesis to analyze phase transitions.
  • Calculation of critical noise, critical exponents, and effective dimension in the thermodynamic limit.

Main Results:

  • Observed second-order phase transitions in the discrete BChS model on BANs.
  • Computed critical noise and exponent ratios as a function of average connectivity.
  • Found the effective dimension to be approximately one and independent of connectivity.
  • Identified similar behavior on directed BANs, Erdös-Rènyi random graphs (ERRGs), and directed ERRGs (DERRGs).

Conclusions:

  • The discrete BChS model exhibits second-order phase transitions on BANs with critical behavior dependent on average connectivity.
  • The model's universality class on BANs differs from its directed counterpart (DBANs) across all studied connectivities.
  • The findings provide insights into opinion formation on heterogeneous networks and highlight the role of network structure.