Another phase transition in the Axelrod model

TL;DR

This paper explores how changing the neighborhood size in Axelrod's cultural dissemination model reveals a new phase transition, complementing the known transition related to the number of traits, and provides a mean-field analysis.

Contribution

It introduces the effect of neighborhood radius variation on the Axelrod model and identifies a new phase transition, expanding understanding of its complex behavior.

Findings

Discovered a new phase transition at a critical neighborhood radius R.

Mapped a q -- R phase diagram for the model.

Provided a mean-field approximation for infinite lattice analysis.

Abstract

Axelrod's model of cultural dissemination, despite its apparent simplicity, demonstrates complex behavior that has been of much interest in statistical physics. Despite the many variations and extensions of the model that have been investigated, a systematic investigation of the effects of changing the size of the neighborhood on the lattice in which interactions can occur has not been made. Here we investigate the effect of varying the radius R of the von Neumann neighborhood in which agents can interact. We show, in addition to the well-known phase transition at the critical value of q, the number of traits, another phase transition at a critical value of R, and draw a q -- R phase diagram for the Axelrod model on a square lattice. In addition, we present a mean-field approximation of the model in which behavior on an infinite lattice can be analyzed.