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.

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.

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.

Heat capacity and monogamy relations in the mixed-three-spin XXX Heisenberg model at low temperatures

2016 ◽  
Vol 14 (05) ◽  
pp. 1650020
Author(s):  
Hamid Arian Zad ◽  
Hossein Movahhedian
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Phase Transitions ◽  
Homogeneous Magnetic Field ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Tripartite Entanglement ◽  
Separable States

Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant [Formula: see text] and spins (1/2,1/2) have coupling constant [Formula: see text]. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants [Formula: see text] and [Formula: see text]. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.

scholarly journals SUPERCONDUCTING PHASE TRANSITION IN THE NAMBU–JONA-LASINIO MODEL

2001 ◽  
Vol 16 (17) ◽  
pp. 1129-1138 ◽  
Author(s):  
M. SADZIKOWSKI
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Superconducting Phase ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Rich Phase ◽  
Quark Interaction ◽  
Quark Coupling ◽  
Superconducting Phase Transition

The Nambu–Bogoliubov–de Gennes method is applied to the problem of superconducting QCD. The effective quark–quark interaction is described within the framework of the Nambu–Jona-Lasinio model. The details of the phase diagram are given as a function of the strength of the quark–quark coupling constant G′. It is found that there is no superconducting phase transition when one uses the relation between the coupling constants G′ and G of the Nambu–Jona-Lasinio model which follows from the Fierz transformation. However, for other values of G′ one can find a rich phase structure containing both the chiral and the superconducting phase transitions.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

EFFECTS OF TEMPERATURE-DEPENDENT COUPLING CONSTANT EVOLUTION ON THE UNIFICATION SCALE

1987 ◽  
Vol 02 (07) ◽  
pp. 479-485 ◽  
Author(s):  
K. ENQVIST ◽  
K. KAJANTIE
Keyword(s):  
Gauge Coupling ◽  
Coupling Constants ◽  
Thermal Bath ◽  
Coupling Constant ◽  
Temperature Dependent ◽  
Cosmological Context ◽  
Effects Of Temperature

We discuss how the evolution of gauge coupling constants is affected by a thermal bath, the existence of which is natural to assume in a cosmological context. The temperature dependent renormalization prescription induced by the thermal bath can cause sizeable effects, and the unification scale is shifted from the value computed from the coupling constant evolution in vacuum.

scholarly journals Dynamics and the emergence of geometry in an information mesh

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Philip Tee
Keyword(s):  
Ground State ◽  
Quantum Particle ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Graph Properties ◽  
Graph Theoretical Approach ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Ground State Geometry ◽  
The Continuum

Abstract The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle.

scholarly journals Variational Solutions of the Hubbard Model for the bcc Lattice

1990 ◽  
Vol 43 (3) ◽  
pp. 333
Author(s):  
CM Villet ◽  
W-H Steeb
Keyword(s):  
Phase Transitions ◽  
Hubbard Model ◽  
Ground State ◽  
Second Phase ◽  
Coupling Constant ◽  
Magnetic Structures ◽  
Bcc Lattice ◽  
Variational Solutions ◽  
Band Filling ◽  
Neutral Case

A variational method is used to find approximative solutions of the Hubbard model for the ground state of the bcc lattice in the weak and strong coupling limits. The neutral case (a half-filled band) is found to be antiferromagnetic for all values of the coupling constant. However, for other choices of the band� filling second phase transitions between different magnetic structures are found if the coupling constant is varied.

Sign in / Sign up

Export Citation Format

Share Document