Another phase transition in the Axelrod model

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.

A novel analytical formulation of the Axelrod model

“…Although the Axelrod model is usually studied through numerical simulations, different analytical approaches were developed based on stochastic equations [3,12] or deterministic systems [14,13], that describe the evolution of the density of bonds with a given similarity and provide some insights about the origin of the phase-transition. However, these approaches rely on several approximations needed to discard high-order terms and make equations analytical tractable.…”