  We argue that when a social convergence mechanism exists and is strong
enough, one should expect the emergence of a well defined "field", i.e. a
slowly evolving, local quantity around which individual attributes fluctuate in
a finite range. This condensation phenomenon is well illustrated by the
Deffuant-Weisbuch opinion model for which we provide a natural extension to
allow for spatial heterogeneities. We show analytically and numerically that
the resulting dynamics of the emergent field is a noisy diffusion equation that
has a slow dynamics. This random diffusion equation reproduces the long-ranged,
logarithmic decrease of the correlation of spatial voting patterns empirically
found in [1, 2]. Interestingly enough, we find that when the social cohesion
mechanism becomes too weak, cultural cohesion breaks down completely, in the
sense that the distribution of intentions/opinions becomes infinitely broad. No
emerging field exists in this case. All these analytical findings are confirmed
by numerical simulations of an agent-based model.
