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.

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.

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.

SUSCEPTIBILITY SINGULARITIES AT FIRST-ORDER PHASE TRANSITIONS

1992 ◽  
Vol 03 (05) ◽  
pp. 1071-1082 ◽  
Author(s):  
D.B. ABRAHAM ◽  
P.J. UPTON
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Phase Transitions ◽  
Thermodynamic Functions ◽  
Infinite Number ◽  
Limit Point ◽  
Correlation Functions ◽  
Negative Real Axis ◽  
First Order ◽  
First Order Phase

Problems associated with analyticity of thermodynamic functions close to first-order phase transitions are briefly reviewed. The bubble model for correlation functions is then applied to planar Ising-like models at subcritical temperatures (T<Tc) with a bulk magnetic field h. The fluctuation sum is used to calculate the susceptibility χ(h) from the bubble correlation function. We show that χ(h), calculated this way, must contain an essential singularity at h=0 i.e. at the first-order phase boundary. This has important implications to metastability, where we demonstrate that if the ensemble is restricted such that the magnetization stays positive when h goes negative, χ(h) has an infinite number of poles along the negative real axis with a limit-point at h=0. For an unrestricted ensemble, a Yang-Lee circle theorem is derived.

scholarly journals Скачкообразные процессы магнитного разупорядочения, стимулированные магнитным полем в системах со структурной неустойчивостью

2020 ◽  
Vol 62 (5) ◽  
pp. 710
Author(s):  
В.И. Вальков ◽  
А.В. Головчан ◽  
В.В. Коледов ◽  
Б.М. Тодрис ◽  
В.И. Митюк
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Static Magnetic Fields ◽  
First Order ◽  
Temperature Dependences ◽  
Second Order Transition ◽  
First Order Phase ◽  
Experimental Pressure ◽  
The Magnetic Field ◽  
Theoretical Results

A theoretical analysis of the features of structural and magnetostructural first-order phase transitions in magnetocaloric helimagnetic alloys of the Mn_{1-x}Cr_{x}NiGe system has been carried out. To describe the observed displacive structural transitions hex(P6_{3}/mmc)<->orth(P_{nma}), we used the local soft mode model in the approximation of a biased harmonic oscillator. In the absence of a magnetic field, the emergence of a helimagnetic order as a structurally induced second-order transition was described in the framework of the Heisenberg model, taking into account the dependence of the exchange integrals on the structural order parameters and elastic strains. In the presence of a magnetic field, it was found that the approximation of the characteristic temperatures for the helimagnetic HM(P_{nma}) and lability temperatures of the hexagonal paramagnetic PM(P6_{3}/mmc) states, due to the influence of the magnetic field, leads to the appearance of previously unexplored peripheral magnetostructural first-order phase transitions with insignificant magnetization jumps that increase with increasing magnetic induction.In this case, as the pressure increases to 4 kbar with constant induction of the magnetic field, the peripheral transitions transform into reversible first-order magnetostructural transitions, and at even higher pressures (10-14 kbar) into full-fledged first-order magnetostructural transitions with magnetization jumps comparable with maximum value of magnetization. Experimental pressure studies of the temperature dependences of magnetization in static magnetic fields with an induction of up to 1 T and a pressure of up to 14 kbar confirm the theoretical results.

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.

scholarly journals To a Question about First-Order Phase Transitions in Orthoferrites

2016 ◽  
Vol 17 (2) ◽  
pp. 193-197
Author(s):  
O.G. Medvedovs’ka ◽  
G.K. Chepurnykh ◽  
T.O. Fedorenko ◽  
S.V. Sokolov
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
External Magnetic Field ◽  
Landau Theory ◽  
Second Order ◽  
First Order ◽  
First Order Phase

On the example of first-order phase transitions in orthoferrites under the influence of an external magnetic field is shown the effectiveness of the application of the Landau theory of phase transitions, commonly used in second-order phase transitions. This is especially important when used Hamiltonian is a function of many variables.

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