  We consider the mean-field classical Heisenberg model and obtain detailed
information about the total spin of the system by studying the model on a
complete graph and sending the number of vertices to infinity. In particular,
we obtain Cramer- and Sanov-type large deviations principles for the total spin
and the empirical spin distribution and demonstrate a second-order phase
transition in the Gibbs measures. We also study the asymptotics of the total
spin throughout the phase transition using Stein's method, proving central
limit theorems in the sub- and supercritical phases and a nonnormal limit
theorem at the critical temperature.
