  How does immigrant integration in a country change with immigration density?
Guided by a statistical mechanics perspective we propose a novel approach to
this problem. The analysis focuses on classical integration quantifiers such as
the percentage of jobs (temporary and permanent) given to immigrants, mixed
marriages, and newborns with parents of mixed origin. We find that the average
values of different quantifi?ers may exhibit either linear or non-linear growth
on immigrant density and we suggest that social action, a concept identified by
Max Weber, causes the observed non- linearity. Using the statistical mechanics
notion of interaction to quantitatively emulate social action, a unified
mathematical model for integration is proposed and it is shown to explain both
growth behaviors observed. The linear theory instead, ignoring the possibility
of interaction effects would underestimate the quantifiers up to 30% when
immigrant densities are low, and overestimate them as much when densities are
high. The capacity to quantitatively isolate different types of integration
mechanisms makes our framework a suitable tool in the quest for more efficient
integration policies.
