  We derive an exact expression for the partition function of the su(m)
Haldane-Shastry spin chain, which we use to study the density of levels and the
distribution of the spacing between consecutive levels. Our computations show
that when the number of sites N is large enough the level density is Gaussian
to a very high degree of approximation. More surprisingly, we also find that
the nearest-neighbor spacing distribution is not Poissonian, so that this model
departs from the typical behavior for an integrable system. We show that the
cumulative spacing distribution of the model can be well approximated by a
simple functional law involving only three parameters.
