  Spin glass models with quadratic-type Hamiltonians are disordered statistical
physics systems with competing ferromagnetic and anti-ferromagnetic spin
interactions. The corresponding Gibbs measures belong to the exponential family
parametrized by (inverse) temperature $\beta>0$ and external field
$h\in\mathbb{R}$. Given a sample from these Gibbs measures, a statistically
fundamental question is to infer the temperature and external field parameters.
In 2007, Chatterjee (Ann. Statist. 35 (2007), no.5, 1931-1946) first proved
that in the absence of external field $h=0$, the maximum pseudolikelihood
estimator for $\beta$ is $\sqrt{N}$-consistent under some mild assumptions on
the disorder matrices. It was left open whether the same method can be used to
estimate the temperature and external field simultaneously. In this paper,
under some easily verifiable conditions, we prove that the bivariate maximum
pseudolikelihood estimator is indeed jointly $\sqrt{N}$-consistent for the
temperature and external field parameters. The examples cover the classical
Sherrington-Kirkpatrick model and its diluted variants.
