  The study of the effects of spatially uniform fields on the steady-state
properties of Axelrod's model has yielded plenty of controversial results. Here
we re-examine the impact of this type of field for a selection of parameters
such that the field-free steady state of the model is heterogeneous or
multicultural. Analyses of both one and two-dimensional versions of Axelrod's
model indicate that, contrary to previous claims in the literature, the steady
state remains heterogeneous regardless of the value of the field strength.
Turning on the field leads to a discontinuous decrease on the number of
cultural domains, which we argue is due to the instability of zero-field
heterogeneous absorbing configurations. We find, however, that spatially
nonuniform fields that implement a consensus rule among the neighborhood of the
agents enforces homogenization. Although the overall effects of the fields are
essentially the same irrespective of the dimensionality of the model, we argue
that the dimensionality has a significant impact on the stability of the
field-free homogeneous steady state.
