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We use the mean-field approximation based on the Bogoliubov inequality to study the ferrimagnetic mixed spin-1 and spin-5/2 Blume–Emery–Griffiths (BEG) model on a hypercube lattice. The effects of the equal crystal field D = DA = DB and the ratio of biquadratic and bilinear exchange interactions R = K/|J| are examined by extracting the phase diagrams on the (R = K/|J|; T = 1/z|J|) and (D/z|J|; T = 1/z|J|) planes, respectively. Additionally, we have drawn the phase diagrams in the (DA/z|J|; T = 1/z|J|) and (DB/z|J|; T = 1/z|J|) planes for various values of the ratio R = K/|J| (R > 0). Our phase diagrams show both first- and second-order transitions, as well as tricritical points. It is evident that the system can exhibit single and double compensation temperatures. Finally, the temperature dependencies of the total and sublattice magnetizations present a few outstanding features. [ABSTRACT FROM AUTHOR]

The magnetic properties, phase diagrams, and hysteresis behavior of a spin-3/2 Blume–Capel multilayer system are studied using the Monte Carlo Simulation. First, we have established the ground-state phase diagrams for T = 0 K. Then, we have plotted the thermal variations of the two sublattices and total magnetizations, as well as the corresponding phase diagrams in order to investigate the effects of some Hamiltonian parameters, namely the exchange interactions, the crystal field, and the number of layers. Finally, we have analyzed the hysteresis behavior where there is the formation of one or three loops. This study shows the appearance of a certain number of features, especially the existence of second- and first-order phase transition border lines and critical isolated end points. [ABSTRACT FROM AUTHOR]

We have used the real-space Migdal-Kadanoff renormalization group technique on d-dimensional hypercubic lattice to study the mixed spin-1/2 and spin-2 Blume-Capel model. First, we indicate a critical dimension dC ≈ 2.05, above and below which different topologies of phase diagrams occur. The phase diagrams have been plotted in the (crystal field, temperature) plane around dC, in which there is a second-order phase transition. Moreover, using the variation of the free energy at low temperatures, we have established the ground-state phase diagrams in the (∆/J, C/J) plane for d < dC and d ≥ dC. In particular, we have seen the appearance of two first-order transitions at very low temperatures by the use of the free energy and its isotherm derivative. A detailed analysis of fixed points and flow diagrams indicates that there is no tricritical point. [ABSTRACT FROM AUTHOR]

The mixed spin-1 and spin-3/2 Blume-Emery-Griffiths model with attractive biquadratic coupling is investigated in the framework of the Migdal-Kadanoff Renormalization Group method. By changing the ratio R > 0 of biquadratic and bilinear exchange interactions and according to the different values of crystal field interactions, we have determined six main types of phase diagrams. The full flow in the parameters space of the Hamiltonian was established and the fixed points obtained are drawn up in a table. In addition, we have determined the eigenvalues of the transformation of the group in the vicinity of the critical points. Finally, the introduction of a positive biquadratic interaction was discussed. [ABSTRACT FROM AUTHOR]