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.

PHASE TRANSITIONS OF THE MIXED-SPIN ISING MODEL ON A DECORATED LATTICE WITH THE NEAREST-NEIGHBOR INTERACTION BETWEEN DECORATING SPINS

2009 ◽  
Vol 23 (24) ◽  
pp. 4963-4976 ◽  
Author(s):  
A. BENYOUSSEF ◽  
A. EL KENZ ◽  
M. EL YADARI ◽  
M. LOULIDI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nearest Neighbors ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Neighbor Interaction ◽  
Mixed Spin

A mean-field approximation is developed for a decorated ferrimagnetic Ising model, in which the two magnetic atoms A and B have spins σ=1/2 and S=1, respectively. In this system, the exchange interaction between nearest-neighbors of atom B is taken into account. Some interesting phenomena, such as the appearance of three types of phase diagrams and the existence of one and two compensation points are found. Phase diagrams and temperature dependence of the magnetizations of the system are investigated in detail.

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.

SURFACE PHASE DIAGRAMS OF SEMI-INFINITE FERRIMAGNETIC SYSTEM

2021 ◽  
pp. 2150025
Author(s):  
SAIDA ZOUHAIR ◽  
MOHAMED MONKADE ◽  
ABDELMOUMEN EL ANTARI ◽  
MOHAMMED EL BOUZIANI ◽  
NABIL HACHEM ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Mean Field ◽  
Three Dimensional ◽  
Exchange Interactions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Surface Exchange ◽  
Crystal Fields ◽  
First Order Phase

The three-dimensional semi-infinite mixed spin-1/2 and spin-3/2 ferrimagnetic Ising system with crystal field is investigated using the mean-field approximation and the Monte Carlo simulation. According to the ratio [Formula: see text] of bulk and surface exchange interactions and the ratio [Formula: see text] of bulk and surface crystal fields, we have classified four qualitative types of phase diagrams characterized by the presence or absence of ordinary, extraordinary, surface and special phase transitions. The critical behavior of the surface and bulk magnetizations has also been highlighted in the vicinity of these different transitions. At low temperatures, two critical end-points appear in the bulk and on the surface in the ordered region limiting two successive first-order phase transitions. Furthermore, we have made a comparison with other works on similar models in pure or mixed versions.

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.

Magnetic properties and phase diagrams of the mixed spin-(1 2, 3 2) Ising–Heisenberg model in the mean field approximation

2021 ◽  
pp. 2150486
Author(s):  
G. Seto ◽  
R. A. A. Yessoufou ◽  
A. Kpadonou ◽  
E. Albayrak ◽  
F. Hontinfinde
Keyword(s):  
Phase Diagrams ◽  
Heisenberg Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Quadrupole Moments ◽  
New Approach ◽  
Crystal Fields ◽  
Mixed Spin ◽  
The Mean

In this paper, the effects of the longitudinal [Formula: see text] and the transverse [Formula: see text] crystal fields on the mixed spin-[Formula: see text] Ising–Heisenberg model have been studied. The thermodynamic properties of the model are obtained by using a new approach of the mean field approximation (MFA). The thermal variations of the order-parameters and the total magnetic susceptibility of the model are carefully investigated to obtain the phase diagrams on the [Formula: see text] planes for [Formula: see text] and on the [Formula: see text] planes for [Formula: see text] and 6. The existence of compensation temperatures between the sublattice magnetizations, [Formula: see text], and the two components of the quadrupole moments, [Formula: see text], are observed. Our results are compared with other existing works in the literature and reliable agreements are found.

Partially Disordered State in the Frustrated Heisenberg Ferrimagnet

2014 ◽  
Vol 215 ◽  
pp. 55-60 ◽  
Author(s):  
Sergey N. Martynov
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Magnetic Phase ◽  
Mean Field ◽  
Exchange Interactions ◽  
Field Approximation ◽  
Magnetic Phase Transitions ◽  
Mean Field Approximation ◽  
The Mean ◽  
Competition Parameter

A model for the description of two-subsystem Heisenberg ferrimagnet with frustrated intersubsystem exchange and competition between exchange interactions in a subsystem is proposed. The conditions of the existence of noncollinear Yafet-Kittel state and partially ordered magnetic structure are investigated. The phase diagram of competition parameter vs temperature is obtained in the mean field approximation. The peculiarities of the succesive magnetic phase transitions are considered.

scholarly journals ISOSPIN LATTICE GAS MODEL AND NUCLEAR-MATTER PHASE DIAGRAM AND PRESSURE-VOLUME ISOTHERMS

1996 ◽  
Vol 05 (02) ◽  
pp. 303-311 ◽  
Author(s):  
T.T.S. KUO ◽  
S. RAY ◽  
J. SHAMANNA ◽  
R.K. SU
Keyword(s):  
Nuclear Matter ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Lattice Gas Model ◽  
Mean Field Approximation ◽  
Kinetic Energy Term ◽  
Phase Liquid ◽  
Matter Phase

We study a cubic lattice gas model for nuclear matter where each lattice site can be either occupied, by one proton or one neutron, or unoccupied. A nearest-neighbor interaction of the form - ∑<ij>Jijτziτzj is assumed. Our model is an isospin-1 Ising model, with τz= (1, 0, –1) representing respectively (proton, vacancy, neutron). A kinetic-energy term has been included in our model. Under the Bragg-Williams mean-field approximation our model exhibits the existence of a dense phase (liquid-like) and a rare phase (gas-like). The nuclear-matter p−v isotherms given by our model are discussed.

A MEAN FIELD STUDY OF THE PHASE TRANSITIONS IN A CLASS OF SYSTEMS WITH COMPLEX ORDER PARAMETERS

1994 ◽  
Vol 08 (28) ◽  
pp. 3963-3986
Author(s):  
EVGENIA J. BLAGOEVA
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Order Parameter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Unconventional Superconductors ◽  
Complex Order ◽  
The Mean ◽  
Expansion Coefficients

A generalized Landau free energy for a complex order parameter expanded up to sixth-order is investigated using group theoretical arguments and the mean-field approximation. Results for the phase transitions that occur are presented. The phase diagram for all allowed values of the expansion coefficients is constructed with an emphasis placed on the influence of the anisotropy in the order parameter space. The results can be used in discussions of unconventional superconductors and modulated structural and magnetic orderings.

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