  Stein's method for concentration inequalities was introduced to prove
concentration of measure in problems involving complex dependencies such as
random permutations and Gibbs measures. In this paper, we provide some
extensions of the theory and three applications: (1) We obtain a concentration
inequality for the magnetization in the Curie--Weiss model at critical
temperature (where it obeys a nonstandard normalization and super-Gaussian
concentration). (2) We derive exact large deviation asymptotics for the number
of triangles in the Erd\H{o}s--R\'{e}nyi random graph $G(n,p)$ when $p\ge0.31$.
Similar results are derived also for general subgraph counts. (3) We obtain
some interesting concentration inequalities for the Ising model on lattices
that hold at all temperatures.
