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Biswas-Chatterjee-Sen Model on Solomon Networks with Two Three-Dimensional Lattices.

Gessineide Sousa Oliveira1, Tayroni Alencar Alves1, Gladstone Alencar Alves2

  • 1Dietrich Stauffer Computational Physics Laboratory, Departamento de Física, Universidade Federal do Piauí, Teresina 64049-550, PI, Brazil.

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|July 26, 2024
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Summary
This summary is machine-generated.

The Biswas-Chatterjee-Sen model shows a second-order phase transition in 3D Solomon networks. Its critical exponents indicate a unique universality class, distinct from lower dimensions and the Ising model.

Keywords:
Monte Carlo simulationsSolomon networksnon-equilibriumphase transition

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Physics

Background:

  • The Biswas-Chatterjee-Sen (BChS) model is a key framework for understanding opinion dynamics.
  • Investigating opinion dynamics on complex network structures is crucial for social science and physics.
  • Previous studies have explored the BChS model on various network dimensions.

Purpose of the Study:

  • To analyze the opinion dynamics of the BChS model on three-dimensional Solomon networks.
  • To determine the nature of the phase transition and calculate critical exponents.
  • To compare the universality class of the 3D BChS model with its lower-dimensional counterparts and the Ising model.

Main Methods:

  • Extensive Monte Carlo simulations were employed to study the BChS model.
  • Finite-size scaling relations were utilized to extrapolate system properties to the thermodynamic limit.
  • Critical exponents for the order parameter, susceptibility, and correlation length were evaluated at the transition point.

Main Results:

  • The BChS model on 3D Solomon networks exhibits a second-order phase transition.
  • Critical exponents were successfully calculated at the phase transition point.
  • The evaluated exponents suggest a distinct behavior compared to 1D and 2D networks.

Conclusions:

  • The BChS model in three dimensions belongs to a different universality class.
  • This 3D universality class is distinct from the BChS model on 1D and 2D Solomon networks.
  • The 3D BChS model also resides in a different universality class compared to the Ising model on the same networks.