  The microcanonical entropy s(e,m) as a function of the energy e and the
magnetization m is computed analytically for the anisotropic quantum Heisenberg
model with Curie-Weiss-type interactions. The result shows a number of
interesting properties which are peculiar to long-range interacting systems,
including nonequivalence of ensembles and partial equivalence. Furthermore,
from the shape of the entropy it follows that the Curie-Weiss Heisenberg model
is indistinguishable from the Curie-Weiss Ising model in canonical
thermodynamics, although their microcanonical thermodynamics in general
differs. The possibility of experimentally realizing quantum spin models with
long-range interactions in a microcanonical setting by means of cold dipolar
gases in optical lattices is discussed.

Statistical Mechanics;Quantum Gases