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

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.