  In this paper, we derive the limit of experiments for one parameter Ising
models on dense regular graphs. In particular, we show that the limiting
experiment is Gaussian in the low temperature regime, non Gaussian in the
critical regime, and an infinite collection of Gaussians in the high
temperature regime. We also derive the limiting distributions of the maximum
likelihood and maximum pseudo-likelihood estimators, and study limiting power
for tests of hypothesis against contiguous alternatives (whose scaling changes
across the regimes). To the best of our knowledge, this is the first attempt at
establishing the classical limits of experiments for Ising models (and more
generally, Markov random fields).
