  It is well known that long-range interactions pose serious problems for the
formulation of statistical mechanics. We show in this paper that ensemble
equivalence is violated in a simple mean-field model of N fully coupled
classical rotators with repulsive interaction (antiferromagnetic XY model).
While in the canonical ensemble the rotators are randomly dispersed over all
angles, in the microcanonical ensemble a bi-cluster of rotators separated by
angle $\pi$, forms in the low energy limit. We attribute this behavior to the
extreme degeneracy of the ground state: only one harmonic mode is present,
together with N-1 zero modes. We obtain empirically an analytical formula for
the probability density function for the angle made by the rotator, which
compares extremely well with numerical data and should become exact in the zero
energy limit. At low energy, in the presence of the bi-cluster, an extensive
amount of energy is located in the single harmonic mode, with the result that
the energy temperature relation is modified. Although still linear, $T = \alpha
U$, it has the slope $\alpha \approx 1.3$, instead of the canonical value
$\alpha =2$.
