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