The microcanonical and the canonical phase diagrams of the mean-field Blume-Emery-Griffiths model

The mean-field Blume-Emery-Griffiths model is studied both in the microcanonical ensemble and in the canonical ensemble in this paper. In the microcanonical ensemble, when the bilinear exchange interaction J <= 0 and the single-spin energy parameter Delta is in the range of 0.5 <= Delta less than or similar to 0.12, the system exhibits an entropy jump at the phase transition point, causing the zerothorder phase transition. On the contrary, when.. > 0, there will not be any zeroth-order phase transitions. In addition, we show four different kinds of microcanonical (Delta, T) phase diagrams and give their corresponding ranges of the parameter... Six different kinds of canonical (Delta, T) phase diagrams and their corresponding boundaries of the parameter.. are given in this paper as well. Moreover, we demonstrate that (Delta, T) phase diagrams are all the same for any J <= 0 in the microcanonical ensemble or in the canonical ensemble, respectively.

Automated summary

The mean-field Blume-Emery-Griffiths model is studied in both the microcanonical and canonical ensembles. In the microcanonical ensemble, a zeroth-order phase transition occurs when J <= 0 and 0.5 <= Delta <= 0.12, resulting in an entropy jump at the phase transition point. Conversely, there are no zeroth-order phase transitions when... > 0. Four different microcanonical (Delta, T) phase diagrams and their respective parameter ranges are shown. Six different canonical (Delta, T) phase diagrams and their corresponding parameter boundaries are also presented. Additionally, it is demonstrated that (Delta, T) phase diagrams are identical for any J <= 0 in either the microcanonical or canonical ensemble.