  We study dipolarly coupled three dimensional spin systems in both the
microcanonical and the canonical ensembles by introducing appropriate numerical
methods to determine the microcanonical temperature and by realizing a
canonical model of heat bath. In the microcanonical ensemble, we show the
existence of a branch of stable antiferromagnetic states in the low energy
region. Other metastable ferromagnetic states exist in this region: by
externally perturbing them, an effective negative specific heat is obtained. In
the canonical ensemble, for low temperatures, the same metastable states are
unstable and reach a new branch of more robust metastable states which is
distinct from the stable one. Our statistical physics approach allows us to put
some order in the complex structure of stable and metastable states of dipolar
systems.
