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We explore ensemble inequivalence in long-range interacting systems bystudying an XY model of classical spins with ferromagnetic and nematiccoupling. We demonstrate the inequivalence by mapping the microcanonical phasediagram onto the canonical one, and also by doing the inverse mapping. We showthat the equilibrium phase diagrams within the two ensembles strongly disagreewithin the regions of first-order transitions, exhibiting interesting featureslike temperature jumps. In particular, we discuss the coexistence and forbiddenregions of different macroscopic states in both the phase diagrams.

Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings