Non-monotonicity and divergent time scale in Axelrod model dynamics

FEDERICO VAZQUEZ; SIDNEY REDNER

EUROPHYSICS LETTERS

EPL ASSOCIATION

Año: 2007 vol. 78 p. 18002 - 18002

0295-5075

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 individualpossesses 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 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 .