Zeroth-order phase transition in the Blume-Emery-Griffiths model without bilinear exchange coupling.

We study the simplified Blume-Emery-Griffiths model without bilinear exchange coupling both in the microcanonical ensemble and in the canonical ensemble. This model can exhibit a zeroth-order phase transition in the microcanonical ensemble accompanied by a finite entropy jump. However, this singularity in entropy cannot be observed in the canonical ensemble, which illustrates the ensemble inequivalence. Moreover, the global phase diagram of this model is given in both ensembles.