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.


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