Global culture: A noise-induced transition in finite systems

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 $r\lesssim T^{-1}$ induces monocultural configurations, whereas $r\gtrsim T^{-1}$ sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.