  We study $N$-particle systems in R^d whose interactions are governed by a
hypersingular Riesz potential $|x-y|^{-s}$, $s>d$, and subject to an external
field. We provide both macroscopic results as well as microscopic results in
the limit as $N\to \infty$ for random point configurations with respect to the
associated Gibbs measure at scaled inverse temperature $\beta$. We show that a
large deviation principle holds with a rate function of the form
`$\beta$-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 $\beta$, the limiting density for
$s>d$ is strongly $\beta$-dependent.
