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

Abstract

Using the repulsive Blume–Emery–Griffiths model, we compute the phase diagram in three field spaces, temperature (T), crystal field (Δ), 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, Δ) 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.

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

“…In principle, two-state Ising model is analytically solvable under the nearest neighbor lattice interaction approximation. However, the real systems can be complex and the spin may be more than two-value, and this situation gives birth to a variation of the original Ising model, the so-called Blume-Emery-Griffiths (BEG) model in dealing with the problem of phase transitions of He 3 -He 4 mixtures [69][70][71], wherein the spin is three-value. In general, a n-state BEG model is such an Ising model that describes a system with n different particles.…”