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arXiv:cond-mat/0409276 · International Journal of Modern Physics B

PHASE DIAGRAMS OF THE SPIN-1 BLUME–EMERY–GRIFFITHS MODEL IN A RANDOM TRANSVERSE FIELD

Hamid Ez-zahraouy A, H. Mahboub, A. Benyoussef, Mohamed Jamil Ouazzani

Published Dec 30, 2004• 6 citations
arXivHTMLPDF

Abstract

The effect of the random quantum transverse field Ω on the tricritical behavior of the spin-1 Blume–Emery–Griffiths (BEG) model is studied using an effective field theory. It is found that the tricritical behavior depends on both the biquadratic interaction K, single-ion anisotropy Δ and the concentration p of the disorder of Ω. Indeed, there exists a special value p1 of the probability p below which the tricritical behavior disappears. In addition, at sufficiently low temperatures, the system exhibits long-range order accompanied by the tricritical behavior below a special value p2 of the probability p.

DOI
10.1142/s021797920402775x

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理论物理通讯：英文版•Jan 1, 2003•0 citations
The effect of the random quantum transverse field Ω on the tricritical behavior of the spin-1 Blume–Emery–Griffiths (BEG) model is studied using an effective field theory. It is found that the tricritical behavior depends on both the biquadratic interaction K, single-ion anisotropy Δ and the concentration p of the disorder of Ω. Indeed, there exists a special value p1 of the probability p below which the tricritical behavior disappears. In addition, at sufficiently low temperatures, the system exhibits long-range order accompanied by the tricritical behavior below a special value p2 of the probability p.
The effect of the random quantum transverse field ΩΩΩ on the tricritical behavior of the spin-1 Blume- Emery- Griffiths (BEG) model is studied using effective field theory. It is found, that the tricritical behavior depends on both the biquadratic interaction KKK, single- ion anisotropy ΔΔΔ, and the concentration ppp of the disorder of ΩΩΩ. Indeed, there exist a special value p1p_{1}p1​ of the probability ppp below which the tricritical behavior disappears.
We have studied the effects of the random transverse single-ion anisotropy in the phase diagram and in the thermodynamic properties of the spin−1 Blume–Capel quantum model, which has been used the approach the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The phase diagrams were obtained in the temperature τ=kBT∕zJ versus single-ion anisotropy δx=Dx∕zJ plane for several values of δy=Dy∕zJ, p and q. The results show that there is a tricritical behavior only in the range of δy given by −0.048≤δy<0.5. This behavior is shown again by the curves of the magnetization m as a function of temperature τ with corresponding values of δy, p and q.
The critical behavior and the magnetic properties of the spin 3/2 Blume-Emery-Griffiths model have been investigated on a square lattice within the framework of an effective field theory based on the use of a probability distribution technique. The effect of the transverse crystal field D(x) on the magnetic properties is examined. The model presents very rich critical behavior, which includes first and second order phase transitions. The tricritical, isolated critical, and critical end points are also observed.
In this work, we investigate the thermodynamic properties of the quantum Blume-Capel model with spin S=5/2 S = 5/2 S=5/2 in the presence of transverse and random crystalline fields. The system is described by a Hamiltonian that includes ferromagnetic exchange interactions between nearest neighbors, a longitudinal single-ion anisotropy, and a transverse single-ion anisotropy. Using a mean-field approach based on Bogoliubov's inequality for the Gibbs free energy, we derive the fundamental thermodynamic potential and the equation of state for the magnetization. The influence of the longitudinal and transverse anisotropy parameters on the magnetic ordering and phase transitions is analyzed in detail. We present magnetization versus temperature diagrams for various combinations of the anisotropies, exploring both positive and negative values. Our results reveal that the system exhibits standard second-order phase transitions for most parameter ranges, with no evidence of tricritical behavior. However, for certain positive values of the anisotropies, the model displays a first-order phase transition within the ordered phase, characterized by a jump from a higher-spin ordered state to a lower-spin ordered state. The critical temperatures are shown to be sensitive to the magnitude and sign of the anisotropy parameters. In particular, negative transverse anisotropies favor magnetic order, raising the critical temperature, while positive anisotropies promote disorder, lowering the critical temperature. This study provides a comprehensive analysis of the phase diagram of the S=5/2 S = 5/2 S=5/2 quantum Blume-Capel model and highlights the role of transverse fields in modifying the critical behavior.
We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.
We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.