Erd\"os-R\'enyi phase transition in the Axelrod model on complete graphs

TL;DR

This paper demonstrates that the Axelrod model exhibits a second order phase transition on complete graphs, analogous to the Erd"os-Rényi transition, with the transition influenced by the initial interaction probability related to parameters F and Q.

Contribution

It reveals a new phase transition in the Axelrod model on complete graphs and links it to the Erd"os-Rényi transition, highlighting the role of initial interaction probability.

Findings

Identifies a second order phase transition in the Axelrod model at F→∞ on complete graphs.

Shows the transition is equivalent to Erd"os-Rényi network transition.

Highlights the importance of initial interaction probability in sparse topologies.

Abstract

The Axelrod model has been widely studied since its proposal for social influence and cultural dissemination. In particular, the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters, $F$ and $Q$. In this work, we show that the Axelrod model undergoes a second order phase transition in the limit of $F \rightarrow \infty $ on a complete graph. This transition is equivalent to the Erd\"os-R\'enyi phase transition in random networks when it is described in terms of the probability of interaction at the initial state, which depends on a scaling relation between $F$ and $Q$. We also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter $F$.