Random crystal field effects on antiferromagnetic spin-1 Blume–Capel model

2021 ◽  
pp. 2150286
Author(s):  
Erhan Albayrak
Keyword(s):  
Crystal Field ◽  
Critical Points ◽  
Bethe Lattice ◽  
Honeycomb Lattice ◽  
Recursion Relations ◽  
First Order ◽  
Field Effects ◽  
Number Formula ◽  
First Order Phase ◽  
Antiferromagnetic Spin

The outcome of the random crystal field effects on the antiferromagnetic spin-1 Blume–Capel model and external magnetic field are examined on the Bethe Lattice in terms of exact recursion relations. It is assumed that the crystal field is either turned on or off randomly with probability [Formula: see text] and [Formula: see text], respectively. The phase diagrams are constructed from the thermal analysis of the order parameters with the coordination number [Formula: see text] which corresponds to honeycomb lattice. It is explored that the system goes both second- and first-order phase transitions, along with the reentrant behavior and a few critical points. The reentrant behavior is stronger for lower values of [Formula: see text] and disappears as [Formula: see text] gets closer to 1.0. The first-order lines are observed to be either linked to the tricritical points or decomposed. The critical end points and double critical points are also observed.

Trimodal-random field Blume-Capel model

2021 ◽  
pp. 2150270
Author(s):  
Erhan Albayrak
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Random Field ◽  
Phase Diagrams ◽  
Critical Points ◽  
Bethe Lattice ◽  
Recursion Relations ◽  
First Order ◽  
Random Magnetic Field ◽  
First Order Phase

The external random magnetic field [Formula: see text] with three nodes, i.e. acting up and down along the [Formula: see text]-axis and zero, effective on the spins in the Blume-Capel model is analyzed on the Bethe lattice in terms of the exact recursion relations. All the nodes are assumed to have the same probability, [Formula: see text], so that the model could give various kinds of phase transitions. As a mapping of the phase transitions, the phase diagrams are constructed on two different planes which present very rich and interesting phase diagrams. In addition to the second- and first-order phase transitions, a few critical points, reentrant and double reentrant behaviors are also observed.

THE SPIN-1 BLUME–CAPEL MODEL WITH ALTERNATINGLY CHANGING BILINEAR EXCHANGE INTERACTIONS BETWEEN SUBLATTICES

2012 ◽  
Vol 26 (05) ◽  
pp. 1250031 ◽  
Author(s):  
ERHAN ALBAYRAK
Keyword(s):  
Crystal Field ◽  
Nearest Neighbor ◽  
Bethe Lattice ◽  
Exchange Interactions ◽  
Coordination Numbers ◽  
First Order ◽  
Crystal Fields ◽  
Negative Crystal ◽  
First Order Phase ◽  
Second Order Phase Transition

The spin-1 Blume–Capel model is studied on a Bethe lattice which is divided into two sublattices A and B. Alternatingly changing bilinear exchange interactions, JAB and JBA, between the sublattices, i.e., between the nearest-neighbor shell spins, are assumed. The phase diagrams of the model are studied on the (JAB, T) planes for given values of JBA, crystal fields D and the coordination numbers q = 3, 4 and 6. It was found that the model either displays only second-order phase transition lines at higher crystal field values or second- and first-order phase transitions lines combined at tricritical points at lower negative crystal fields. It was also found that the tricritical points move to higher temperatures and to higher values of JAB as the crystal field becomes more negative.

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 mixed spin-1/2 and spin-1 model with alternating coordination number

2019 ◽  
Vol 33 (11) ◽  
pp. 1950102
Author(s):  
Erhan Albayrak
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Coordination Number ◽  
Bethe Lattice ◽  
Recursion Relations ◽  
Coordination Numbers ◽  
First Order ◽  
Mixed Spin ◽  
Phase Transition Temperatures ◽  
First Order Phase

The mixed spin-1/2 and spin-1 Blume–Capel model is studied with randomly alternated coordination numbers (CN) on the Bethe lattice (BL) by utilizing the exact recursion relations. Two different CNs are randomly distributed on the BL by using the standard–random (SR) approach. It is observed that this model presents first-order phase transitions and tricritical points for variations of CNs 3 and 4, even if these behaviors are not displayed for the regular mixed-spin on the BL. The phase diagrams are mapped by obtaining the phase transition temperatures of the first- and second-order on several planes.

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 CRYSTAL-FIELD EFFECTS IN THE FIRST-ORDER VALENCE TRANSITION IN YbInCu4 INDUCED BY EXTERNAL MAGNETIC FIELD

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3306-3306 ◽  
Author(s):  
M. DZERO
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Crystal Field ◽  
Valence Transition ◽  
First Order ◽  
Field Effects ◽  
Wide Range

As it was shown earlier [Dzero, Gor'kov and Zvezdin, J. Phys.: Condens. Matt.12, L711 (1000)], the properties of the first-order valence phase transition in YbInCu4 in the wide range of magnetic fields and temperatures are perfectly described in terms of a simple entropy transition for free Yb ions. Within this approach, the crystal field effects have been taken into account and we show that the phase diagram in the B - T plane acquires some anisotropy with respect to the direction of an external magnetic field.

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