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.

References in corpus (2)

• Statistical physics of social dynamics
• Divergent Time Scale in Axelrod Model Dynamics

Cited by in corpus (6)

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• Erdös-Rényi phase transition in the Axelrod model on complete graphs
• Non-equilibrium phase transition and cultural drift in the continuous-trait Axelrod model
• Leaders and obstacles raise cultural boundaries