A study of the bilayer Bethe lattice for spin- Ising model

Albayrak, Erhan; Yılmaz, Sait; Akkaya, Seyma

doi:10.1016/j.jmmm.2006.07.031

Cited by 24 publications

(27 citation statements)

References 47 publications

(35 reference statements)

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“…The reentrant behavior is seen when the model presents two Néel temperatures for q = 4 and 6 only. Now we present a brief discussion of what we have found: (i) The same GS configurations are found with those of the FM/FM interactions for spin-3/2 model [8], but with different GS phase diagrams. (ii) The first-order phase transitions are always seen for transitions from phase IV, i. e. compensated phase, to P phase, the paramagnetic phase, as shown in figures 3d, e, g and i.…”

Section: Discussionsupporting

confidence: 57%

“…Even though the multilayer structures containing spin-1/2 or spin-1 have attracted a great deal of interest, the multilayered spin-3/2 models have not received enough attention, i. e. we could only report a few works; the two-layered model with competing interactions was studied by using the interfacial approximation on a square lattice [7], a bilayer Bethe lattice with FM/FM interactions by the use of the recursion relations [8] and on a model with the periodical arrangement of one layer with spin-1/2 and the other layer with spin-3/2 were examined by the use of the effective field theory [9]. We should note that the external magnetic field and bilinear interaction parameter are always in competition for the AFM systems, i. e. the spins in a nearest-neighbor (NN) pair for the AFM system are aligned oppositely but the external magnetic field tries to align them parallelly.…”

Section: Introductionmentioning

confidence: 99%

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The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Albayrak

Akkaya

Cengiz

2009

Journal of Magnetism and Magnetic Materials

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Two-layer Bethe lattice whose lattice sites are occupied with spin-3/2 atoms is solved exactly by using the recursion relations in a pairwise approach for given coordination numbers q = 3, 4 and 6 with equal external magnetic fields acting on the layers. The ferromagnetic (FM) and antiferromagnetic (AFM) interactions for the spins of the upper and lower layers, respectively, and either FM or AFM type interactions between the adjacent spins of the layers are assumed. The phase diagrams of the model are studied on different planes for given system parameters by obtaining the ground state (GS) phase diagrams and the thermal variations of the order parameters and the response functions, i. e. the susceptibility and the specific heat, in detail. It was found that the model presents both second-and first-order phase transitions. The reentrant behavior is seen when the model presents two Néel temperatures for higher q values. The existence of the tricritical point and critical end points is also confirmed.

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Section: Discussionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Albayrak

Akkaya

Cengiz

2009

Journal of Magnetism and Magnetic Materials

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“…(ii) The first-order phase transitions are always seen for transitions from phase IV, i. e. compensated phase, to P phase, the paramagnetic phase, as shown in figures 3d, e, g and i. (iii) The tricritical points and critical end points are found here in contrast to the case with FM/FM interactions [8]. (iv) The reentrant behavior is only exhibited for transitions from phase III to phase I or IV for both q = 4 and 6 and is only seen for q = 6 for the phase transitions from phase V to phase I.…”

Section: Discussionmentioning

confidence: 61%

Spin-3/2 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Albayrak¹,

Yigit²

2009

Condens. Matter Phys.

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“…Thus in this pairwise approach [30,35,36], three exact recursion relations are defined as the ratios of these partition functions of the separate branches on the bilayer Bethe lattice as (1 2, 1 2) e (1 2, 1 2)…”

Section: Introductionmentioning

confidence: 99%

The FM/AFM bilayer Bethe lattice with FM or AFM interlayer interactions

Albayrak

2008

Physica Status Solidi (b)

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The bilayer Bethe lattice with the Ising spins of the top layer having only ferromagnetic (FM) interactions and the spins of the bottom one having only antiferromagnetic (AFM) interactions were allowed to interact via the interlayer interaction either FM or AFM type. The problem was analyzed by using the exact recursion relations in a pairwise approach for given coordination numbers q = 3, 4 and 6 with equal external magnetic fields acting on the layers. The phase diagrams of the model were obtained on different planes for given system parameters by studying the ground state (GS) phase diagrams and the thermal variations of the order parameters and the response functions, i.e. the susceptibility and the specific heat, in detail. The model with five distinct GS configurations presents only the second‐order phase transition lines, i.e. the lines of the Néel temperatures TN. Two TN's were obtained for q = 6 in the transition regions from the AFM phases to the FM phases at low temperatures, as a result the TN lines show reentrant behavior for q = 6. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A study of the bilayer Bethe lattice for spin- Ising model

Cited by 24 publications

References 47 publications

The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Spin-3/2 Ising model on a two-layer Bethe lattice with FM/AFM interactions

The FM/AFM bilayer Bethe lattice with FM or AFM interlayer interactions

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