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.

Magnetic properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Rachidi Yessoufou ◽  
Saliou Amoussa ◽  
Felix Hontinfinde
Keyword(s):  
Magnetic Properties ◽  
Phase Transitions ◽  
Crystal Field ◽  
Cayley Tree ◽  
Second Order ◽  
Coordination Numbers ◽  
First Order ◽  
Mixed Spin ◽  
Second Order Transition ◽  
Zero Values

AbstractWe use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ1 and Δ2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D A = Δ1/J,D B = Δ2/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D A or D B increases. The first-order transitions only exist for some appropriate non-zero values of D A and/or D B. The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β 0 of the model is estimated and found to be ¼ at small values of D A = D B = D and β 0 = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.

THE CRYSTAL FIELD EFFECTS ON THE PHASE DIAGRAMS OF THE SPIN-2 BILAYER BETHE LATTICE

2008 ◽  
Vol 22 (27) ◽  
pp. 4877-4898 ◽  
Author(s):  
ERHAN ALBAYRAK ◽  
SEYMA AKKAYA ◽  
SABAN YILMAZ
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Bethe Lattice ◽  
Interlayer Coupling ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Temperature Dependent ◽  
Field Interaction

The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J1 and J2, interlayer coupling constant between the layers J3 and crystal field interaction Δ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J2/|J1|, J3/q|J1|) planes for given Δ values and on the (Δ/qJ, J3/qJ) plane when J1 = J2 = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J1 > 0, J2 > 0, and for J3 > 0 or J3 < 0 on the (kT/J1, J3/J1) planes for given Δ/qJ1 and J2/J1 and on the (Δ/J, kT/J) plane for given J3/J when J1 = J2 = J for the coordination number q = 3. It was found that the system exhibits both first- and second-order phase transitions and tricritical points. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments.

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 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.

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.

scholarly journals INFLUENCE OF PRESSURE ON SMECTIC A-NEMATIC PHASE TRANSITION

1999 ◽  
Vol 13 (09n10) ◽  
pp. 275-283 ◽  
Author(s):  
KISOR MUKHOPADHYAY ◽  
PRABIR K. MUKHERJEE
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Phenomenological Model ◽  
Order Parameter ◽  
Nematic Phase ◽  
Tricritical Point ◽  
Second Order ◽  
Experimental Results ◽  
First Order ◽  
Smectic A

We propose a Landau-de Gennes phenomenological model to describe the pressure induced smectic A-nematic phase transition. The influence of pressure on smectic A-nematic phase transitions are discussed for varying coupling between orientational and translational order parameter with pressure. Increasing the pressure, the first order nematic-smectic A transition becomes second order at a tricritical point which agrees fairly well with available experimental results.

scholarly journals Fate of false vacua in holographic first-order phase transitions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Aldo L. Cotrone ◽  
Angel Paredes
Keyword(s):  
Phase Transitions ◽  
Chiral Symmetry ◽  
Metastable Phase ◽  
Chiral Symmetry Breaking ◽  
Model Parameters ◽  
Temperature Phase ◽  
Thin Wall ◽  
Critical Temperatures ◽  
First Order ◽  
First Order Phase

Abstract Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the derivative term in the effective bounce action, that was missing in the literature. Then, we address the full problem within the top-down Witten-Sakai-Sugimoto model. It displays both a confinement/deconfinement and a chiral symmetry breaking/restoration phase transition which, depending on the model parameters, can happen at different critical temperatures. For the confinement/deconfinement case we perform the numerical analysis of an effective description of the transition and also provide analytic expressions using thick and thin wall approximations. For the chiral symmetry transition, we implement a variational approach that allows us to address the challenging non-linear problem stemming from the Dirac-Born-Infeld action.

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.

Some Remarks on Phase Transitions Generated by the Superposition of Multifractals

1997 ◽  
Vol 11 (24) ◽  
pp. 2961-2974
Author(s):  
H. J. Chen ◽  
H. C. Tseng ◽  
W. Y. Lai ◽  
W. D. Chen
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Second Order

Emergence of novel second-order phase transitions by sums of multifractals was found by Radons and Stoop.1,2 Using the same method as Radons and Stoop but different support, we have found that the second-order phase transitions are suppressed.3 In this paper, we continue to extend the method to three multifractals, with the effect of the sums of the three multifractals being the sums of two identical multifractals and those of two different multifractals combined together. We have found that the resulted phase diagrams are more complicated, with second-order phase transitions either partially or completely suppressed.

Coulomb interaction energy including overlap effects for the ground state of RbCs beyond 7 Å

1996 ◽  
Vol 74 (3-4) ◽  
pp. 155-158
Author(s):  
K. Hussein
Keyword(s):  
Interaction Energy ◽  
Coulomb Interaction ◽  
Configuration Space ◽  
Ground State ◽  
Present Method ◽  
Second Order ◽  
Experimental Results ◽  
Coulomb Energy ◽  
First Order ◽  
Dispersion Terms

We use a perturbative model based on a partition of the configuration space into four regions to calculate the Coulomb energy including charge-overlap effects (induction and dispersion terms) for the interaction between two atoms Rb(5s2S) and Cs(6s2S). Results for first-order electrostatic as well as second-order induction and dispersion energies will be presented in the range 13 < R < 25 a.u. The damping functions for the various dispersion terms varying as R−6, R−8, and R−10 in the range of large R have also been determined, and fitted analytical forms will be displayed for these terms. From comparison with accurate experimental results, the present method is seen to be valid for values of R beyond 7 Å (1 Å = 10−10 m).

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