  In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic
interactions and the associated spin chain of Haldane-Shastry type introduced
by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use
this result and the freezing trick to derive a simple analytic expression for
the partition function of the Frahm-Inozemtsev chain. We show that the energy
levels of the latter chain can be written in terms of the usual motifs for the
Haldane-Shastry chain, although with a different dispersion relation. The
formula for the partition function is used to analyze the behavior of the level
density and the distribution of spacings between consecutive unfolded levels.
We discuss the relevance of our results in connection with two well-known
conjectures in quantum chaos.
