Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of an external magnetic field on a complete graph

Using the repulsive Blume-Emery-Griffiths model, we compute the phase diagram in three field spaces, temperature (T), crystal field (Delta), and magnetic field (H) on a complete graph in the canonical and microcanonical ensembles. For low biquadratic interaction strengths (K), a tricritical point exists in the phase diagram where three critical lines meet. As K decreases below a threshold value (which is ensemble dependent), new multicritical points such as the critical end point and the bicritical end point arise in the (T, Delta) plane. For K > -1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K = -1, the two critical lines in the H plane disappear, and as K decreases further, there is no phase transition in the H plane. At exactly K = -1, the two ensembles become equivalent. Beyond that, for all K < -1, there are no multicritical points, and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K, i.e. for attractive biquadratic interaction. We find that the transition lines in the H plane are not monotonic in temperature for large positive values of K.

Automated summary

This study used the repulsive Blume-Emery-Griffiths model to calculate the phase diagram in three field spaces, and investigated the properties of critical points and multicritical points under different interaction strengths. The results showed that the phase diagram and critical points exhibit different behaviors under different conditions.