Phase Diagram of the Nagel-Kardar Model in the Microcanonical-Canonical Crossover

Many models with long-range interactions, including the Nagel-Kardar (NK) model, have been proposed to demonstrate and explore the differences between microcanonical ensembles and canonical ensembles. In the NK model, the first-order phase transition always accompanied by the temperature jump in the microcanonical ensemble, while this anomalous temperature jump can not be observed in the canonical ensemble. Moreover, the tricritical points of this model are different from each other in these two different ensembles. In this paper, the microcanonical-canonical crossover behavior of the NK model is studied by placing the NK model in contact with a two-level reservoir, and transition of the tricritical point is presented.