Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

2007 ◽  
Vol 62 (3-4) ◽  
pp. 127-139 ◽  
Author(s):  
M. Ali Pınar ◽  
Mustafa Keskin ◽  
Ahmet Erdinç ◽  
Osman Canko
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Mean Field ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Critical Behaviour ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Cluster Variation

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

THE COUPLED SPIN-1 BLUME-CAPEL SUBLATTICES WITH DIFFERENT BILINEAR INTERACTIONS

2012 ◽  
Vol 26 (08) ◽  
pp. 1250042
Author(s):  
ERHAN ALBAYRAK ◽  
AHMET ERDINÇ
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Crystal Fields ◽  
D Values

The equilibrium properties of the spin-1 Blume-Capel model are studied by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The lattice is divided into two sublattices A and B, and different bilinear interaction parameters JAB and JBA between the nearest-neighbor spins are assumed. The temperature variations of the order-parameters are studied, therefore, the phase diagrams are obtained on the (JAB, T) planes for given values of JBA and crystal fields D. It was found that the model yields both second- and first-order phase transitions at higher positive D values and the lines of which combine at tricritical points. Negative values of D lead only second-order phase transitions. The phase diagrams are symmetric under the exchange of JAB with JBA as expected.

APPLICATION OF THE GENETIC ALGORITHM TO BLUME–EMERY–GRIFFITHS MODEL: TEST CASES

2005 ◽  
Vol 19 (28) ◽  
pp. 4229-4237 ◽  
Author(s):  
OSMAN CANKO ◽  
MEHMET ŞAHİN ◽  
AHMET ERDİNÇ
Keyword(s):  
Genetic Algorithm ◽  
Mean Field ◽  
Stable State ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Simulation Techniques ◽  
Beg Model ◽  
Optimal Approach

The equilibrium properties of the Blume–Emery–Griffiths (BEG) model Hamiltonian with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) are studied using the genetic algorithm technique. Results are compared with lowest approximation of the cluster variation method (CVM), which is identical to the mean field approximation. We found the genetic algorithm to be very efficient for fast search at the average fraction of the spins, especially in the early stages as the system is far from the equilibrium state. A combination of the genetic algorithm followed by one of the well-tested simulation techniques seems to be an optimal approach. The curvature of the inverse magnetic susceptibility is also presented for the stable state of the BEG model.

The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurgül Seferoğlu ◽  
Bülent Kutlu
Keyword(s):  
Phase Diagram ◽  
Cellular Automaton ◽  
Mean Field ◽  
Anisotropy Parameter ◽  
Cluster Variation Method ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variation Method ◽  
Ferrimagnetic Phase ◽  
Creutz Cellular Automaton

AbstractThe Blume-Emery-Griffiths model is simulated using the cooling algorithm which is improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The simulations are carried out on a simple cubic lattice at K/J = −1.5 in the range of −3.5 < D/J < 0.5, with J and K representing the nearestneighbour bilinear and biquadratic interactions, D being the single-ion anisotropy parameter. The phase diagram characterizing phase transition of the model is obtained. We found different kinds of phase transitions between the ferromagnetic, quadrupolar, staggered quadrupolar and ferrimagnetic phases for K/J = −1.5. In particular, the region of the phase diagram containing a ferrimagnetic phase is explored and compared to those obtained by other methods. The simulations confirm that the ferrimagnetic phase occurs in the narrow interval −3.006 ≤ D/J < −3. This result is in a good agreement with Monte Carlo renormalization group and closer to the cluster variation method result than the mean field approximation result.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

Chiral condensate of cold dense quark matter with external magnetic field

2020 ◽  
Vol 35 (19) ◽  
pp. 2050160
Author(s):  
Song Shi ◽  
Juan Liu
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
External Magnetic Field ◽  
Quark Matter ◽  
Chemical Potential ◽  
Field Approximation ◽  
Chiral Condensate ◽  
Mean Field Approximation ◽  
Dynamical Mass ◽  
Dense Quark Matter

At zero temperature and finite chemical potential, the gap equation of cold dense quark matter under external magnetic field is studied with NJL model in the mean-field approximation. By introducing new methods, it is found that the Nambu phase has sophisticated structures which have not been studied before. As a consequence, the phase diagram is expanded and divided into five areas, in each area the condensate has unique behaviors with chemical potential varying. Furthermore, the expanded phase diagram is used to predict the order of phase transition between the Nambu phase and the Wigner phase, it can also be used to explain the relations of dynamical mass and chemical potential. Meanwhile, the metastable states and cascade effect of dynamical mass are studied in this paper.

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