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

## TL;DR

This paper studies a model on multi-dimensional networks and finds a second-order phase transition across all dimensions.

## Contribution

The study reveals that the model's critical exponents vary with dimension, indicating no upper critical dimension.

## Key findings

- The model exhibits a second-order phase transition for all dimensions 1 ≤ D ≤ 6.
- Critical exponents deviate from mean-field values and depend on the dimension D.
- Scaling regime was achieved despite limitations in simulating larger networks.

## Abstract

The discrete version of the Biswas–Chatterjee–Sen model, defined on D-dimensional hypercubic Solomon networks, with 1≤D≤6, has been studied by means of extensive Monte Carlo simulations. Thermodynamic-like variables have been computed as a function of the external noise probability. Finite-size scaling theory, applied to different network sizes, has been utilized in order to characterize the phase transition of the system in the thermodynamic limit. The results show that the model presents a phase transition of the second order for all considered dimensions. Despite the lower critical dimension being zero, this dynamical system seems not to have any upper critical dimension since the critical exponents change with D and go away from the expected mean-field values. Although larger networks could not be simulated because the number of sites drastically increases with the dimension D, the scaling regime has been achieved when computing the critical exponent ratios and the corresponding critical noise probability.