SPIN-2 ISING MODEL ON THE BILAYER BETHE LATTICE

2008 ◽  
Vol 22 (24) ◽  
pp. 4189-4203 ◽  
Author(s):  
ERHAN ALBAYRAK ◽  
SEYMA AKKAYA ◽  
SABAN YILMAZ
Keyword(s):  
Phase Diagrams ◽  
Ground State ◽  
Nearest Neighbor ◽  
Lower Layer ◽  
Bethe Lattice ◽  
Branching Ratio ◽  
Interlayer Coupling ◽  
Coupling Constants ◽  
First Order Phase ◽  
Over The Top

A spin-2 system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins was analyzed by the use of the exact recursion relations in a pairwise approach. The upper layer interacting with nearest-neighbor (NN) bilinear interaction J1 is laid over the top of the lower layer interacting with bilinear NN interaction J2, and the two layers are tied together via the bilinear interaction between the vertically aligned adjacent NN spins denoted as J3. The study of the ground state phase diagrams on the (J2/|J3|, J1/|J3|) plane with J3>0 and J3<0 and on the (J2/J1, J3/q J1) plane with J1>0 has yielded five distinct ground state configurations. The temperature dependent phase diagrams are obtained for the case with intralayer coupling constants of the two layers with ferromagnetic type J1 and J2>0, and the interlayer coupling constant of the layers with either ferromagnetic J3>0 or antiferromagnetic type J3<0 on the (kT/J1, J3/J1) planes for given values of the J2/J1 for various values of the coordination numbers. As a result, we have found that the model presents both second- and first-order phase transitions, therefore, tricritical points.

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.

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.

scholarly journals Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

2019 ◽  
Vol 21 (11) ◽  
pp. 6216-6223 ◽  
Author(s):  
Daniel Silva ◽  
Per Arne Rikvold
Keyword(s):  
Phase Diagrams ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
State Diagrams ◽  
Solid Foundation

The fifteen topologically different zero-temperature phase diagrams in the model's full, five-dimensional parameter space provide a solid foundation for studies at finite temperatures.

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.

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.

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.

scholarly journals Ground State Searches in Fcc Intermetallics

1991 ◽  
Vol 253 ◽  
Author(s):  
C. Wolverton ◽  
G. Ceder ◽  
D. De Fontaine ◽  
H. Dreyssé
Keyword(s):  
Perturbation Method ◽  
Phase Diagrams ◽  
Cluster Expansion ◽  
Ground State ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Linear Constraints ◽  
Coherent Potential Approximation ◽  
Potential Approximation ◽  
Configurational Energy

ABSTRACTA cluster expansion is used to predict the fcc groutnd states, i.e., the stable phases at zero Kelvin as a function of composition, for alloy systems. TFile internetallic structures are not assumed, but derived rigorously by minimizing the configurational energy subject to linear constraints. This ground state search includes pair and multiplet interactions which spatially extend to fourth nearest neighbor. A large number of these concentration-independent interactions are computed by the method of direct configurational averaging using a linearizedmuffin- tin orbital Hamiltonian cast into tight binding form (TB-LMTO). The interactions, derived without the use of any adjustable or experimentally obtained parameters, are compared to those calculated via the generalized perturbation method extention of the coherent potential approximation within the context of a KKR Hamiltonian (KKR-CPA-GPM). Agreement with the KKR-CPA-GPM results is quite excellent, as is the comparison of the ground state results with the fcc-based portions of the experimentally-determined phase diagrams under consideration.

scholarly journals Time-Resolved Investigation of the Molecular Chemiluminescence SrI(A2∏1/2,3,2,B2∑+→X2∑+) and the Atomic Resonance Fluorescence Sr(53P1→51S0) Following The Pulsed Dye Laser Generation Of Sr(53PJ) in the Presence of CF3I

1995 ◽  
Vol 16 (2) ◽  
pp. 121-138 ◽  
Author(s):  
S. Antrobus ◽  
D. Husain ◽  
Jie Lei ◽  
F. Castaño ◽  
M. N. Sanchez Rayo
Keyword(s):  
Ground State ◽  
Branching Ratio ◽  
Atomic Emission ◽  
Electronic Energy ◽  
Dye Laser ◽  
Pulsed Dye Laser ◽  
Laser Generation ◽  
Buffer Gas ◽  
Resonance Fluorescence ◽  
Time Resolved

A time-resolved investigation is presented of the electronic energy distribution in SrI following the collision of the optically metastable strontium atom, Sr [5s5p(3PJ)], with the molecule CF3I. Sr[5s5p(3PJ)], 1.807 eV above its 5s2(1S0) electronic ground state, was generated by pulsed dye-laser excitation of ground state strontium vapour to the Sr(53P1) state at , λ =689.3 nm {Sr(53P1←51S0)} at elevated temperature (840 K) in the presence of excess helium buffer gas in which rapid Boltzmann equilibration within the 53PJ spin-orbit manifold takes place. Time resolved atomic emission from Sr(53P1→51S0) at the resonance transition and the molecular chemiluminescence from SrI(A2∏1,2,3/2,B2∑+→X2∑+) resulting from reaction of the excited atom with CF3I were recorded and shown to be exponential in character. SrI in the A2∏1/2,3/2 (172.5, 175.4 kJ mol-1) and B2∑+ (177.3 kJ mol-1) states are energetically accessible on collision by direct-I-atomic abstraction between Sr(3P) and CF3I. The first-order decay coefficients for the atomic and molecular emissions are found to be equal under identical conditions and hence SrI(A2∏1/2,3/2, B2∑+) are shown to arise from direct I- atom abstraction reactions. The molecular systems recorded were SrI (A2∏1/2→X2∑+, Δv=0, λ=694 nm), SrI(A2∏3/2→X2∑+, Δv=0, λ=677 nm) and SrI(B2∑+→X2∑+) (Δv=0, λ=674 nm), dominated by the Δv=0 sequences on account of Franck-Condon considerations. The combination of integrated m61ecular and atomic intensity measurements yields estimates of the branching ratios into the specific electronic states, A1/2, A3/2 and B, arising from Sr(53PJ)+CF3I which are found to be as follows: A1/2,1.2 × 10-2; A3/2, 6.7 × 10-3; B, 5.1 × 10-3 yielding ∑SrI(A1/2+A3/2+B)=2.4 × 10-2. As only the X, A and B states SrI are accessible on reaction, assuming that the removal of Sr(53PJ) occurs totally by chemical removal, this yields an upper limit for the branching ratio into the ground state of ca. 98%. The present results are compared with previous time-resolved measurements on excited states of strontium halides that we have reported on various halogenated species resulting from reactions of Sr(53PJ), together with analogous chemiluminescence studies on Sr(3PJ) and Ca(43PJ) from molecular beam measurements.

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