  We study mean-field classical $N$-vector models, for integers $N\ge 2$. We
use the theory of large deviations and Stein's method to study the total spin
and its typical behavior, specifically obtaining non-normal limit theorems at
the critical temperatures and central limit theorems away from criticality.
Important special cases of these models are the XY ($N=2$) model of
superconductors, the Heisenberg ($N=3$) model (previously studied in \cite{KM}
but with a correction to the critical distribution here), and the Toy ($N=4$)
model of the Higgs sector in particle physics.
