Ordering phase transition in the one-dimensional Axelrod model

TL;DR

This paper investigates a one-dimensional cellular automaton model for cultural dynamics, revealing a phase transition between uniform and diverse cultural states, analyzed through mean-field and reaction-diffusion approaches.

Contribution

It introduces a detailed analysis of the ordering phase transition in the 1D Axelrod model, combining numerical and mean-field methods to understand its non-equilibrium behavior.

Findings

Identifies a phase transition between ordered and disordered cultural states.

Shows the transition point varies with initial disorder distribution.

Uses mean-field approximation to qualitatively capture the phenomenology.

Abstract

We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.