Biswas-Chatterjee-Sen Model Defined on Solomon Networks in (1 ≤ D ≤ 6)-Dimensional Lattices

Area of Science:

• Statistical Physics
• Complex Networks
• Dynamical Systems

Background:

• The Biswas-Chatterjee-Sen model is a discrete dynamical system.
• Understanding phase transitions in complex networks is crucial.
• Hypercubic Solomon networks provide a framework for studying network dynamics.

Purpose of the Study:

• To analyze the phase transition of the discrete Biswas-Chatterjee-Sen model on D-dimensional hypercubic Solomon networks.
• To determine the critical behavior and critical exponents for varying dimensions (1≤D≤6).
• To investigate the influence of external noise probability on the system's dynamics.

Main Methods:

• Extensive Monte Carlo simulations were employed.
• Thermodynamic-like variables were computed as a function of external noise probability.
• Finite-size scaling theory was applied to analyze the phase transition in the thermodynamic limit.

Main Results:

• The model exhibits a second-order phase transition for all investigated dimensions.
• The system appears to lack an upper critical dimension as critical exponents change with D.
• Critical exponent ratios and critical noise probability were determined, achieving the scaling regime.

Conclusions:

• The Biswas-Chatterjee-Sen model on hypercubic Solomon networks demonstrates complex phase transition behavior.
• The dimensionality of the network significantly influences the critical exponents, deviating from mean-field predictions.
• Further research on higher dimensions is limited by computational resources but the scaling regime was established.