Ensemble inequivalence in a generalized XY model

In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.