The nature of the continuous non-equilibrium phase transition of Axelrod's model

Instituto de Física de São Carlos, Universidade de São Paulo - Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

Received: 11 July 2015
Accepted: 24 August 2015

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 in which 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 . Using Monte Carlo simulations and finite-size scaling we show that the mean density of cultural domains μ is an order parameter of the model that vanishes as with at the critical point. In addition, for the correlation length critical exponent we find and for Fisher's exponent, . This set of critical exponents places the continuous phase transition of Axelrod's model apart from the known universality classes of non-equilibrium lattice models.