Polarization inhibits the phase transition of Axelrod's model

TL;DR

This paper investigates how polarization affects Axelrod's model of cultural dissemination, showing that polarization suppresses the phase transition in large systems and influences the system's state depending on network percolation thresholds.

Contribution

The study introduces a polarized feature into Axelrod's model and demonstrates its impact on phase transitions and system states through numerical and mean-field analyses.

Findings

Polarization eliminates the phase transition in the thermodynamic limit.

Finite systems exhibit a polarized or multicultural phase depending on network percolation.

The stationary state is influenced by the network's percolation threshold.

Abstract

We study the effect of polarization in Axelrod's model of cultural dissemination. This is done through the introduction of a cultural feature that takes only two values, while the other features can present a larger number of possible traits. Our numerical results and mean-field approximations show that polarization reduces the characteristic phase transition of the original model to a finite-size effect, since at the thermodynamic limit only the ordered phase is present. Furthermore, for finite system sizes, the stationary state depends on the percolation threshold of the network where the model is implemented: a polarized phase is obtained for percolation thresholds below 1/2, a fragmented multicultural one otherwise.