Global culture:: A noise-induced transition in finite systems -: art. no. 045101

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural frozen configurations are found not to be stable. This general result is proven rigorously in d = 1, where the dynamics is described in terms of a Lyapunov potential. In d = 2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate rless than or similar toT(-1) induces monocultural configurations, whereas rgreater than or similar toT(-1) sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.