Comparison of the ferromagnetic Blume–Emery–Griffiths model and the AF spin-1 longitudinal Ising model at low temperature

Thomaz, M. T.; Silva, E.V. Corrêa

doi:10.1016/j.jmmm.2015.10.071

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…To date, exact solutions have been found for various complex models based on the 1D Ising model. They includes Blume-Emery-Griffiths model [1][2][3] , the model with localized Ising-like spins and exchanging electrons 4 , the models with single-ion anisotropy for the spin-1 chain [5][6][7] or the mixed spin-1/2 and spin-1 Ising chain [8][9][10] , the Ising-Heisenberg "decorated" chains, ladders, and tubes [11][12][13][14][15][16][17][18][19][20] and the Ising-Hubbard diamond chain and ladder 21,22 . These systems show many subtle and important phenomena, including quantized plateaux in the magnetization curves, quantum entanglement, quasi-phases and pseudo-transitions 23 , and describe the properties of real materials, such as the polymeric coordination compounds (see Refs.…”

Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

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Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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“…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%

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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