Non-monotonicity and divergent time scale in Axelrod model dynamics

We study the evolution of the Axelrod model for cultural diversity, a prototypical non-equilibrium process that exhibits rich dynamics and a dynamic phase transition between diversity and an inactive state. We consider a simple version of the model in which each individual possesses two features that can assume q possibilities. Within a mean-field description in which each individual has just a few interaction partners, we find a phase transition at a critical value q c between an active, diverse state for q < q c and a frozen state. For q ≲ q c , the density of active links is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as ( q − q c ) −1/2 .