Tri-critical behavior of the Blume Capel model on a diamond lattice

Santos, J.P.; Barreto, F. C. Sá; Rosa, D. S.

doi:10.1016/j.jmmm.2016.09.086

Cited by 27 publications

(5 citation statements)

References 32 publications

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“…Considering a null external field, we use the same methodology applied in reference [68], and we present the results for the phase diagram 𝑇−𝐷 in figure 1 (a), whose obtained phases are F and P, and also show the named regions d F and d P . Still, in the figure it is possible to verify that for the values of 𝐷 = 0, 𝐷 → ∞, and 𝐷 = −2.772, the temperature values are approximately 𝑇 = 4.0, 6.0, and 2.0, respectively.…”

Section: Numerical Results and Diagramsmentioning

confidence: 99%

“…To obtain the above variational parameter, we must minimize the free energy as presented more in detail in the references [64,68,80]. After the calculations, we obtain expressions for free energy and magnetization, given by…”

Section: Model and Formulationmentioning

confidence: 99%

“…Blume-Emery-Griffiths (BEG) model [54][55][56][57], mixed-spin Ising model [58][59][60][61][62][63] and Blume-Capel (BC) model [64][65][66][67][68][69][70][71][72]. The properties of MCE in the generalized spin-S model were studied by Yüksel and collaborators [73] using the MFT, and by Akinci and collaborators [74] who studied the MCE using the effective-field theory, where they concentrated their studies on continuous phase transitions.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis of magnetic properties and the magnetocaloric effect using the Blume-Capel model

Oliveira¹,

Morais²,

Santos³

et al. 2022

Condens. Matter Phys.

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This work investigates the magnetic properties and the magnetocaloric effect in the spin-1 Blume-Capel model. The study was carried out using the mean-field theory from the Bogoliubov inequality to obtain the expressions of free energy, magnetization and entropy. The magnetocaloric effect was calculated from the variation of the entropy obtained by the mean-field theory. Due to the dependence on the external magnetic field and the anisotropy included in the model, the results for the magnetocaloric effect provided the system with first-order and continuous phase transitions. To ensure the results, the Maxwell relations were used in the intervals where the model presents continuous variations in magnetization and the Clausius-Clapeyron equation in the intervals where the model presents discontinuity in the magnetization. The methods and models for the analysis of a magnetic entropy change and first-order and continuous magnetic phase transitions, such as mean-field theory and the Blume-Capel model, are useful tools in understanding the nature of the magnetocaloric effect and its physical relevance.

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Section: Numerical Results and Diagramsmentioning

confidence: 99%

Section: Model and Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Theoretical analysis of magnetic properties and the magnetocaloric effect using the Blume-Capel model

Oliveira¹,

Morais²,

Santos³

et al. 2022

Condens. Matter Phys.

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show abstract

“…It was also investigated by high-and low-temperatures series expansions [14][15][16], Monte Carlo (MC) simulations [17][18][19][20][21][22] and by position-space renormalization group [23][24][25]. Some variants of the BC model with other spin variables and the presence of disorder in the fields and/or interactions have been objecting of recent studies [26][27][28][29][30][31][32][33]. The existence of a tricritical point (TCP) has been detected in the vicinity of the boundary separating regions with nonzero magnetization from that with zero magnetization through the MFA/EFA solutions and computational simulation.…”

Section: Introductionmentioning

confidence: 99%

The Blume–Capel model on hierarchical lattices: Exact local properties

Rocha-Neto

Camelo-Neto

Nogueira³

et al. 2018

Physica A: Statistical Mechanics and its Applications

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The local properties of the spin one ferromagnetic Blume-Capel model defined on hierarchical lattices with dimension two and three are obtained by a numerical recursion procedure and studied as functions of the temperature and the reduced crystal-field parameter. The magnetization and the density of sites in the configuration S = 0 state are carefully investigated at low temperature in the region of the phase diagram that presents the phenomenon of phase reentrance. Both order parameters undergo transitions from the ferromagnetic to the ordered paramagnetic phase with abrupt discontinuities that decrease along the phase boundary at low temperatures. The distribution of magnetization in a typical profile was determined on the transition line presenting a broad multifractal spectrum that narrows towards the fractal limit (single point) as the discontinuities of the order parameters grow towards a maximum. The amplitude of the order-parameter discontinuities and the narrowing of the multifractal spectra were used to delimit the low temperature interval for the possible locus of the tricritical point.

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“…Maksimov and Kuzemsky [19] studied the cluster generalization of the mean field approximation for the case of a two spin-cluster. The mean field approximation(MFA) was also studied on the Blume-Capel model in a five-site cluster on the diamond lattice from the Bogoliubov inequality [20]. The mean field approximation (MFA) presumes a virtual independence between the spins variables, and the interactions acting in each variable spin like an effective field caused by the nearest neighbours sites [21,22].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

2018

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The mean field approximation results in the mixed spin 1/2 Ising model and spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from the Bogoliubov inequality. The Gibbs free energy, magnetization and critical frontiers are obtained. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states. σ Figure 1: Mixed magnetic nanowire with spin 1/2 Ising in the central column and spin 1 Blume-Capel in the external hexagonal layer.

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Tri-critical behavior of the Blume Capel model on a diamond lattice

Cited by 27 publications

References 32 publications

Theoretical analysis of magnetic properties and the magnetocaloric effect using the Blume-Capel model

Theoretical analysis of magnetic properties and the magnetocaloric effect using the Blume-Capel model

The Blume–Capel model on hierarchical lattices: Exact local properties

Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

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