  We explore ensemble inequivalence in long-range interacting systems by
studying an XY model of classical spins with ferromagnetic and nematic
coupling. We demonstrate the inequivalence by mapping the microcanonical phase
diagram onto the canonical one, and also by doing the inverse mapping. We show
that the equilibrium phase diagrams within the two ensembles strongly disagree
within the regions of first-order transitions, exhibiting interesting features
like temperature jumps. In particular, we discuss the coexistence and forbidden
regions of different macroscopic states in both the phase diagrams.
