The nature of the continuous nonequilibrium phase transition of Axelrod's model

TL;DR

This paper investigates the continuous phase transition in Axelrod's cultural dissemination model on a square lattice, identifying critical exponents and showing it belongs to a unique universality class of nonequilibrium phase transitions.

Contribution

The study provides the first detailed characterization of the critical behavior and universality class of Axelrod's model's phase transition using finite size scaling and Monte Carlo simulations.

Findings

Critical point at q_c = 3.10 ± 0.02

Order parameter exponent β = 0.67 ± 0.01

Correlation length exponent ν = 1.63 ± 0.04

Abstract

Axelrod's model in the square lattice with nearest-neighbors interactions exhibits culturally homogeneous as well as culturally fragmented absorbing configurations. In the case the agents are characterized by $F=2$ cultural features and each feature assumes $k$ states drawn from a Poisson distribution of parameter $q$ these regimes are separated by a continuous transition at $q_c = 3.10 \pm 0.02$. Using Monte Carlo simulations and finite size scaling we show that the mean density of cultural domains $\mu$ is an order parameter of the model that vanishes as $\mu \sim \left ( q - q_c \right)^\beta$ with $\beta = 0.67 \pm 0.01$ at the critical point. In addition, for the correlation length critical exponent we find $\nu = 1.63 \pm 0.04$ and for Fisher's exponent, $\tau = 1.76 \pm 0.01$. This set of critical exponents places the continuous phase transition of Axelrod's model apart from the known universality classes of nonequilibrium lattice models.