Revisiting the effect of external fields in Axelrod's model of social dynamics

TL;DR

This paper re-examines the impact of external fields on Axelrod's social dynamics model, finding that heterogeneous states persist regardless of field strength and that nonuniform fields can induce homogenization, challenging previous claims.

Contribution

It demonstrates that the steady state remains heterogeneous under uniform fields and highlights the stabilizing effect of nonuniform fields implementing a consensus rule.

Findings

Steady states remain heterogeneous regardless of field strength.

Discontinuous decrease in cultural domains with increasing field.

Nonuniform fields promote homogenization.

Abstract

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.