MIXED SPIN-1 AND SPIN-$\frac{3}{2}$ BLUME–CAPEL ISING FERRIMAGNETIC SYSTEM ON THE BETHE LATTICE

2003 ◽  
Vol 17 (07) ◽  
pp. 1087-1100 ◽  
Author(s):  
ERHAN ALBAYRAK
Keyword(s):  
Free Energy ◽  
Curie Temperature ◽  
Phase Diagrams ◽  
Tricritical Point ◽  
Bethe Lattice ◽  
Approximate Methods ◽  
Coordination Numbers ◽  
Mixed Spin ◽  
Quadrupolar Moment

The mixed spin-1 and spin-[Formula: see text] Blume–Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants dA = DA/J for spin-1 and dB = DB/J for spin-[Formula: see text]. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (kTc/J, dA) plane for the central spin are obtained for two different cases; (1) dA = dB and (2) dA is varied for selected values of dB. The results are compared with those of other approximate methods.

EXACT CALCULATION OF THE MAGNETIC SUSCEPTIBILITY AND THE SPECIFIC HEAT OF THE MIXED SPIN-½ AND SPIN-1 SYSTEM ON THE BETHE LATTICE

2004 ◽  
Vol 18 (30) ◽  
pp. 3959-3973 ◽  
Author(s):  
ERHAN ALBAYRAK
Keyword(s):  
Free Energy ◽  
Magnetic Susceptibility ◽  
Specific Heat ◽  
Bethe Lattice ◽  
Order Parameters ◽  
Exact Calculation ◽  
Thermal Behaviors ◽  
Coordination Numbers ◽  
Mixed Spin ◽  
Inverse Susceptibility

The thermal behaviors of the order-parameters, susceptibility and specific heat of the mixed spin-½ and spin-1 Blume–Capel Ising ferrimagnetic system is studied on the Bethe lattice by using the exact recursion equations. The exact equations for the order parameters and the susceptibility are obtained for the sublattices with spin-1 and spin-½. Also, the exact expressions for the free energy and the specific heat are obtained on the Bethe lattice as a whole system. Then the thermal behaviors of the order-parameters, susceptibility, inverse susceptibility and specific heat are studied for the coordination numbers q=4 and q=6. The obtained results are illustrated and discussed in detail.

Critical behaviors and phase diagrams of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising model on the Bethe lattice (BL)

2015 ◽  
Vol 29 (28) ◽  
pp. 1550194 ◽  
Author(s):  
M. Karimou ◽  
R. Yessoufou ◽  
F. Hontinfinde
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Ground State ◽  
Tricritical Point ◽  
Bethe Lattice ◽  
Second Order ◽  
Temperature Phase ◽  
First Order ◽  
Crystal Fields ◽  
Mixed Spin

Using the recursion equations technique, the influences of the single-ion anisotropies or crystal-fields interactions on the magnetic properties of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising ferrimagnetic system are studied on the Bethe lattice (BL). The ground-state phase diagram is constructed, the thermal behaviors of the order-parameters and the free-energy are thoroughly investigated in order to characterize the nature of the phase transitions and to obtain the phase transition temperature. Then, the temperature phase diagrams are obtained in the case of equal crystal-field interactions on the ([Formula: see text] and [Formula: see text]) planes when q = 3, 4 and 6 and in the case of unequal crystal-fields interactions on the ([Formula: see text] and [Formula: see text]) and [Formula: see text] and [Formula: see text]) planes for selected values of [Formula: see text] and [Formula: see text] respectively when q = 3. The model shows first-order and second-order phase transitions, and where the lines are connected is the tricritical point. Besides the first-order and second-order phase transitions, the system also exhibits compensation temperatures depending on appropriate values of the crystal-fields interactions.

Phase diagrams of the random nearest-neighbor mixed spin-1/2 and spin-3/2 Blume–Capel model

2018 ◽  
Vol 32 (27) ◽  
pp. 1850325 ◽  
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Bethe Lattice ◽  
Recursion Relations ◽  
Mixed Case ◽  
Coordination Numbers ◽  
System Parameters ◽  
Mixed Spin ◽  
Critical Lines ◽  
Random Approach

The mixed spin-1/2 and spin-3/2 Blume–Capel (BC) model is considered on the Bethe lattice (BL) with randomly changing coordination numbers (CN) and examined in terms of exact recursion relations. A couple of two different CNs are changed randomly on the shells of the BL in terms of a standard–random approach to obtain the phase diagrams on possible planes of the system parameters. It is found from the thermal analysis of the order-parameters that the model only gives the second-order phase transitions as in the regular mixed case. As the probability of having larger CN increases, the temperatures of the critical lines also increase as expected.

The magnetic phase diagrams of the ternary alloy ABpC1−p on the Bethe lattice

2018 ◽  
Vol 32 (16) ◽  
pp. 1850177
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Diagrams ◽  
Ternary Alloy ◽  
Nearest Neighbor ◽  
Magnetic Phase ◽  
Bethe Lattice ◽  
Recursion Relations ◽  
Coordination Numbers ◽  
First Order ◽  
First Order Phase ◽  
The Given

In this work, the ternary alloy (TA) of the form [Formula: see text] with spin-[Formula: see text], spin-2 and spin-[Formula: see text], respectively, is studied on the Bethe lattice in terms of exact recursion relations in the standard random approach. The bilinear interaction parameter [Formula: see text] is assumed to be ferromagnetic between the nearest-neighbor spins with spin-[Formula: see text] and spin-2, while [Formula: see text] is taken to be antiferromagnetic between spin-[Formula: see text] and spin-[Formula: see text]. The possible phase diagrams are obtained from the thermal analysis of the order parameters for the given coordination numbers z = 3,[Formula: see text]4,[Formula: see text]5 and 6. This analysis has also revealed that the model gives both second- and first-order phase transitions in addition to the compensation temperatures.

The quaternary alloy on the Bethe lattice

2018 ◽  
Vol 32 (21) ◽  
pp. 1850226 ◽  
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Diagrams ◽  
Coordination Number ◽  
Ternary Alloy ◽  
Interaction Parameter ◽  
Bethe Lattice ◽  
Quaternary Alloy ◽  
Spin Models ◽  
Recursion Relations ◽  
Mixed Spin ◽  
Random Approach

The quaternary alloy (QA) is simulated on the Bethe lattice (BL) in the form of ABpCqDr and its phase diagrams are calculated by using the exact recursion relations (ERR) for the coordination number z = 3. The QA is designed on the BL by placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2), C (spin-5/2) or D (spin-1) atoms with probabilities p, q and r, respectively, on the even shells. A compact form of formulation for the QA is obtained in the standard-random approach which can easily be reduced to ternary alloy (TA) and mixed-spin models by the appropriate values of the random variables p, q and r. The phase diagrams are calculated on the temperature and ratio of bilinear interaction parameter planes for given values of probabilities.

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Open Physics ◽  
2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Joël Kplé ◽  
Gabriel Avossevou ◽  
Félix Hontinfinde
Keyword(s):  
Phase Diagrams ◽  
Bethe Lattice ◽  
Model Parameters ◽  
Nearest Neighbour ◽  
Temperature Behaviour ◽  
Recursion Relations ◽  
Crystal Field Strength ◽  
Mixed Spin ◽  
System Configurations ◽  
Very Low Temperature

AbstractTwo layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.

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