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

TL;DR

This paper maps the phase diagram of the repulsive Blume-Emery-Griffiths model on a complete graph, revealing ensemble-dependent multicritical points and phase transition behaviors influenced by biquadratic interaction strength.

Contribution

It provides a detailed analysis of the phase diagram in both ensembles, highlighting the effects of biquadratic interaction strength on critical points and phase transitions.

Findings

Existence of tricritical points for weak biquadratic interaction.

Ensemble dependence of critical lines and multicritical points.

No phase transition in the H plane for K<-1.

Abstract

For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T), crystal field ($\Delta$), and magnetic field (H), is computed on a complete graph, in the canonical and microcanonical ensembles. For weak strength of the biquadratic interaction (K), there exists a tricritical point in the phase diagram where three critical lines meet. As K decreases below a threshold value(which is ensemble dependent), new multicritical points like the critical end point and 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. Exactly at 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 K.