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

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.