  The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of
neural networks and the Ising spin glass are all models of binary data
belonging to the one-parameter exponential family with quadratic sufficient
statistic. Under bare minimal conditions, we establish the
$\sqrt{N}$-consistency of the maximum pseudolikelihood estimate of the natural
parameter in this family, even at critical temperatures. Since very little is
known about the low and critical temperature regimes of these extremely
difficult models, the proof requires several new ideas. The author's version of
Stein's method is a particularly useful tool. We aim to introduce these
techniques into the realm of mathematical statistics through an example and
present some open questions.
