Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth-order critical point

The canonical phase diagram of the Blume-Emery-Griffiths model with infinite-range interactions is known to exhibit a fourth-order critical point at some negative value of the biquadratic interaction K < 0. Here we study the microcanonical phase diagram of this model for K < 0, extending previous studies which were restricted to positive K. A fourth-order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth-order critical point is studied in detail revealing some distinct features from the canonical counterpart.