We study N-particle systems in R d whose interactions are governed by a Riesz potential |x − y| −s with an external field in the hypersingular case s > d. We provide both macroscopic results as well as microscopic results in the limit as N → ∞ for random point configurations with respect to the associated Gibbs measure at reciprocal temperature β. We show that a large deviation principle holds with a rate function of the form 'β-Energy +Entropy', yielding that the microscopic behavior (on the scale N −1/d) of such N-point systems is asymptotically determined by the minimizers of this rate function. In contrast to the asymptotic behavior in the integrable case s < d, where on the macroscopic scale N-point empirical measures have limiting density independent of β, the limiting density for s > d is strongly β-dependent.