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The Axelrod model for the dissemination of culture exhibits a rich spatialdistribution of cultural domains, which depends on the values of the two modelparameters: $F$, the number of cultural features and $q$, the common number ofstates each feature can assume. In the one-dimensional model with $F=q=2$,which is closely related to the constrained voter model, Monte Carlosimulations indicate the existence of multicultural absorbing configurations inwhich at least one macroscopic domain coexist with a multitude of microscopicones in the thermodynamic limit. However, rigorous analytical results for theinfinite system starting from the configuration where all cultures are equallylikely show convergence to only monocultural or consensus configurations. Herewe show that this disagreement is due simply to the order that thetime-asymptotic limit and the thermodynamic limit are taken in the simulations.In addition, we show how the consensus-only result can be derived using MonteCarlo simulations of finite chains.

The consensus in the two-feature two-state one-dimensional Axelrod model revisited