Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies

Madani, M.; Gaye, Abou; Bouziani, M. El; Alrajhi, A.

doi:10.1016/j.physa.2015.06.003

Cited by 21 publications

(9 citation statements)

References 37 publications

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“…The phase diagrams of type II (Figure 7) and of type III (Figure 8) are characterized by the presence of only second-order transitions and they have different shapes (the details of these types will be given below). Similar phase diagrams have been obtained in the BC model with mixed spins (1, 3/2) using a real space renormalization group technique (Madani et al , 2015).…”

Section: Resultssupporting

confidence: 70%

“…Experimentally, the MnNi(EDTA)-6H 2 O complex is an example of a mixed-spin system (Drillon et al , 1983). On the theoretical side, the systems of mixed spins S = 1 and S = 3/2 have been extensively studied by a variety of techniques such as the mean field approximation (Abubrig et al , 2001), the effective field theory (Bobák, 1998a, 2000), the Monte Carlo simulation (Nakamura and Tucker, 2002; Žukovič and Bobák, 2010; Boughazi et al , 2019), the Glauber-type stochastic dynamics (Temizer, 2014), the renormalization group theory (Madani et al , 2015; El Bouziani et al , 2016), the Green's function (Mert, 2012), the exact recursion equations on the Bethe lattice (Albayrak, 2003; Ekiz, 2006) and the cluster variational method in pair approximation (Tucker, 2001).…”

Section: Introductionmentioning

confidence: 99%

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The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

Kihel

Saadi

Aharrouch

et al. 2021

MMMS

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PurposeThe authors investigate the magnetic properties of a mixed spin-3/2 and spin-2 Blume-Capel model on square and cubic lattices with two different single-ion anisotropies.Design/methodology/approachTo study the critical behavior of a mixed spin-3/2 and spin-2 system, the authors have used a real space renormalization group approximation and specifically the Migdal-Kadanoff technique. The authors give the phase diagrams for two different cases: (1) on the (Δ/|J|, 1/|J|) plane with ΔA = ΔB = Δ, and (2) on the (ΔA/|J|, 1/|J|) and (ΔB/|J|, 1/|J|) planes for selected values of ΔB/|J| and ΔA/|J|, respectively.FindingsThe phase diagrams obtained show that the system exhibits both second- and first-order phase transitions as well as tricritical points for some values of the anisotropies. Moreover, using the variation of the free energy and its derivative at low temperatures, the authors have seen the appearance of first-order transitions at very low temperatures.Originality/valueFew investigations of mixed spin-3/2 and spin-2 systems with crystal field have been realized. For this reason, the authors use the renormalization group approach to complete the work done on these systems. In absence of an exact solution, this contributes to the synthesis of the approximation results on mixed spins models.

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Section: Resultssupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

Kihel

Saadi

Aharrouch

et al. 2021

MMMS

Self Cite

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“…For example, the surface performs two different types of second order phase transitions. The first has a temperature higher than that of the bulk; this surface transition is described by the fixed point (O B , C S ), where O B is the fixed point (disorder) of the bulk [48], and C S is that of the surface:…”

Section: Resultsmentioning

confidence: 99%

“…C B is the second order fixed point of the bulk [48], and C Sp the surface one with coordinates C Sp (J S = 1.29,…”

Section: Resultsmentioning

confidence: 99%

“…We have already obtained [48] phase diagrams of the infinite Blume-Capel model (2D and 3D) and the table of fixed points that govern the phases and phase transitions. In the reference [48], the second-order phase transitions are described by the fixed point C, the first order by the fixed point A and the tricritical point by the fixed point T. The various phase diagrams of the infinite model were also obtained according to the ratios of the interactions of the model.…”

Section: H J S S K S S S S C S S Z Zmentioning

confidence: 99%

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Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group

Bouziani¹,

Madani²,

Gaye³

et al. 2016

WJCMP

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We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R 1 and R 2 of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides secondorder transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.

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Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

Antari

Zahir

Hasnaoui³

et al. 2018

Int J Theor Phys

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Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies

Cited by 21 publications

References 37 publications

The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

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