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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. [ABSTRACT FROM AUTHOR]

By using a simple argument, the cause of the thermodynamic non-equivalence of the canonical and microcanonical ensembles is clarified to be the first-order canonical phase transition in the thermodynamic limit. There is ensemble equivalence only when the energy fluctuation is negligible with respect to the average energy. The energy fluctuation does not vanish during the first-order transition even in the thermodynamic limit, so that the ensemble non-equivalence cannot hold anymore. Moreover, similar results can also be derived for other dual ensembles. [ABSTRACT FROM AUTHOR]

A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both. The microcanonical ensemble predicts negative specific heat regions and temperature jumps. Moreover, the global phase diagram of the system is constructed. [ABSTRACT FROM AUTHOR]

The long-range interacting spin-1 chain placed in a staggered magnetic field is studied by means of microcanonical approach. Firstly, we study the microcanonical entropy of the system in the thermodynamic limit and find the system is non-ergodic and can exhibit either first-order phase transition or second-order phase transition by shifting the external magnetic field strength. Secondly, we construct the global phase diagram of the system and find a phase transition area in the phase diagram corresponding to the temperature jump of the first-order phase transition. [ABSTRACT FROM AUTHOR]