Cluster size entropy in the Axelrod model of social influence: small-world networks and mass media

TL;DR

This paper investigates the Axelrod model of social influence using cluster size entropy to identify phase transitions, effects of network topology, and the impact of mass media, revealing new phases and relationships.

Contribution

It introduces the use of cluster size entropy to analyze phase transitions and effects of mass media in the Axelrod model across different network topologies.

Findings

Critical point corresponds to maximum cluster size entropy.

Width of entropy distribution indicates transition order.

Mass media induces a new partially ordered phase.

Abstract

We study the Axelrod's cultural adaptation model using the concept of cluster size entropy, $S_{c}$ that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is unambiguously given by the maximum of the $S_{c}(q)$ distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first- or second-order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait $q_c$ and the number $F$ of cultural features in regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a new partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a new $q-B$ phase diagram for the Axelrod model in regular networks.