Multicritical phase diagrams of the spin- Blume–Emery–Griffiths model on the Bethe lattice using the recursion method

Ekiz, Cesur; Albayrak, Erhan; Keskín, Mustafa

doi:10.1016/s0304-8853(02)00589-9

Cited by 25 publications

(32 citation statements)

References 43 publications

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“…We should also mention that the reentrance also occurs for the second-order phase transition line, which separates the i phase from the f 3/2 phase. A similar phase diagram topology has been obtained in the ferromagnetic spin-3 2 BEG model on the Bethe lattice by using the exact recursion equations by Ekiz et al [12], except for the following differences: (1) the reentrant behaviour has not been observed for the second-order phase transition line which separates the i phase from the f 3/2 phase; (2) the phase boundary between the a and d phases is a first-order phase line.…”

Section: Phase Diagramssupporting

confidence: 71%

“…One should also notice a pronounced reentrance occurring in this diagram. A similar phase diagram has been obtained in the ferromagnetic spin-3 2 BEG model within the MFA [8], the EFT [9] and the CVMPA for the coordination number q < 6 [10], as well as the exact formulation of the model on the Bethe lattice by using the exact recursion equations [12,13] for q < 6, but only differs in that the reentrant behaviour does not exist in these two works. However, the exactly similar phase diagram was obtained for q > 6 in [10] and [13].…”

Section: Phase Diagramssupporting

confidence: 57%

“…This is also a new phase diagram topology in this plane, which is either absent from previous approaches or has gone unnoticed. We should also mention that a similar phase diagram, except for the first-order phase line, has been obtained in a ferromagnetic spin-3 2 BEG model within the CVMPA [10] and the exact formulation of the model on the Bethe lattice by using the exact recursion equations [12]. (a) For K/J = −2.0, in this phase diagram besides the disordered phase (d), the ferromagnetic-3/2 (f 3/2 ) and the ferromagnetic-1/2 (f 1/2 ), ferrimagnetic (i) and antiquadrupolar phase (a) also exist and all the phase boundaries among these phases are second-order lines as seen in Figure 4a.…”

Section: Phase Diagramsmentioning

confidence: 71%

“…Recently, Ekiz et al [12] investigated the ferromagnetic spin- [13] extended the previous work for the presence of an external magnetic field [12]. He presented one phase diagram in the (kT / The purpose of the present paper is to study the temperature dependence of order parameters of the twosublattice ferromagnetic spin-3 2 BEG model for different values of interaction parameters and an external magnetic field, to calculate the global phase diagrams of the spin-3 2 BEG model in the absence and presence of the external magnetic field in detail, and to compare the results with the approximate methods [8 -11] and the exact results on the Bethe lattice [12,13]. These calculations have been carried out by using the lowest approximation of the cluster variation method (LACVM) [14], which is identical with the MFA.…”

Section: Introductionmentioning

confidence: 99%

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Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

Pınar¹,

Keskín

Erdinç³

et al. 2007

Zeitschrift Für Naturforschung A

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The critical behaviour of the ferromagnetic spin-3 2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT /J, K/J), (kT /J, D/J) and (kT /J, H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

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Section: Phase Diagramssupporting

confidence: 71%

Section: Phase Diagramssupporting

confidence: 57%

Section: Phase Diagramsmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

Pınar¹,

Keskín

Erdinç³

et al. 2007

Zeitschrift Für Naturforschung A

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“…The phase diagram sequence in Figs. 1(d)-1(f) is in qualitative topological agreement with Bethe lattice solution [17].…”

Section: Global Phase Diagramsupporting

confidence: 69%

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

et al. 2016

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The spin-3 2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d = 3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d = 3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

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The spin‐3/2 Blume–Emery–Griffiths model with repulsive biquadratic coupling in an external field

Ekiz

2004

Physica Status Solidi (b)

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The spin-3/2 Blume-Emery-Griffiths model is solved on the Bethe lattice in the absence and presence of the external field using the iteration technique (recursion method). The phase diagrams are obtained for the coordination number q = 3, 4, 6 and 8. We confirm the existence of a staggered quadrupolar phase in addition to a ferrimagnetic and ferromagnetic ordered phases and analyze the occurence of re-entrant boundaries inside the ordered region as a character of the coordination of the lattice. A comparison is made with the results of other approximate methods.

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Multicritical phase diagrams of the spin- Blume–Emery–Griffiths model on the Bethe lattice using the recursion method

Cited by 25 publications

References 43 publications

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

The spin‐3/2 Blume–Emery–Griffiths model with repulsive biquadratic coupling in an external field

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