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

Klemm, Konstantin; Eguiluz, Victor M; Toral, Raul; San Miguel, Maxi
Physica A 327, 1-5 (2003)

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.