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.

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.

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 thermal properties of the mixed spin-1/2, 1, 3/2 Ising model on the Bethe lattice

2020 ◽  
pp. 2150079
Author(s):  
J. Kple ◽  
E. Albayrak ◽  
F. Hontinfinde
Keyword(s):  
Thermal Properties ◽  
Magnetic System ◽  
Bethe Lattice ◽  
Thermal Fluctuations ◽  
Model Parameters ◽  
Phase Boundaries ◽  
Recursion Relations ◽  
First Order ◽  
Mixed Spin ◽  
Number Formula

A triple mixed-spin Ising system defined on the Bethe lattice is numerically investigated by means of exact recursion relations (ERRs) calculations. The lattice is constituted by three types of magnetic atoms A, B, C with spins [Formula: see text], [Formula: see text], [Formula: see text] respectively arranged in the form ABCABC. The effects of bilinear exchange and crystal-field interactions as well as those of thermal fluctuations on the order parameters and phase diagrams are thoroughly studied and specified. First-order transitions and tricritical points are present for the coordination number [Formula: see text] whereas at [Formula: see text] they are absent. Global compensation phenomena are absent for the magnetic system. Instead, it is shown that it can only occur between the sublattice magnetizations B and C of the system. Several novel kinds of reentrance of the phase boundaries while varying the values of model parameters have been reported.

scholarly journals Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Cesur Ekiz ◽  
Jozef Strečka ◽  
Michal Jaščur
Keyword(s):  
Magnetic Properties ◽  
Ising Model ◽  
Phase Diagrams ◽  
Bethe Lattice ◽  
Magnetic Behavior ◽  
Recursion Relations ◽  
Mixed Spin

AbstractThe mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.

Triple mixed-spin Ising model

2020 ◽  
Vol 34 (13) ◽  
pp. 2050129
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Magnetic Fields ◽  
Exchange Interaction ◽  
Spin System ◽  
Bethe Lattice ◽  
Nearest Neighbors ◽  
Recursion Relations ◽  
Mixed Spin ◽  
Exchange Interaction Parameter

The A, B and C atoms with spin-1/2, spin-3/2 and spin-5/2 are joined together sequentially on the Bethe lattice in the form of ABCABC[Formula: see text] to simulate a molecule as a triple mixed-spin system. The spins are assumed to be interacting with only their nearest-neighbors via bilinear exchange interaction parameter in addition to crystal and external magnetic fields. The order-parameters are obtained in terms of exact recursion relations, then from the study of their thermal variations, the phase diagrams are calculated on the possible planes of our system. It is found that the model gives only second-order phase transitions in addition to the compensation temperatures.

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.

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.

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