Role of dimensionality in Axelrod's model for the dissemination of culture

We analyze a model of social interaction in one and
two-dimensional lattices for a moderate number of features. We
introduce an order parameter as a function of the overlap between
neighboring sites. In a one-dimensional chain, we observe that the
dynamics is consistent with a second order transition, where the
order parameter changes continuously and the average domain
diverges at the transition point. However, in a two-dimensional
lattice the order parameter is discontinuous at the transition
point characteristic of a first order transition between an
ordered and a disordered state.