Europhysics Letters PREPRINT Non-Monotonicity and Divergent Time Scale in Axelrod Model Dynamics

Abstract.-We study the evolution of the Axelrod model for cultural diversity, a prototypical nonequilibrium 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, there is a phase transition at a critical value qc between an active, diverse state for q < qc and a frozen state. For q <, qc, 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- qc)-1/2. Introduction.- A basic feature of many societies is the tendency for cultural fragmenta-tion, even though individuals may rationally try to reach agreement with acquaintances. A simple yet rich description for this dichotomy is provided by the Axelrod model [1]. Althoughinspired by social science, this model has many similarities with classical non-equilibrium processes of coarsening and dynamical transitions, such as the kinetic Ising model [2], the votermodel [3], and birth-death processes [4]. In the Axelrod model, each individual carries a set of F characteristic features--for exam-ple, one's preferences for sports, for music, for food, etc--that can assum