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In this work, we studied the magnetic properties and hysteresis behavior of the ferromagnetic spin-3/2 Blume–Capel model with a transverse crystal field in a graphene monolayer. For this purpose, the mean-field approximation based on the Gibbs–Bogoliubov inequality for the free energy was used. We examined the effects of some physical parameters of the system, namely, the longitudinal and transverse crystal fields, external magnetic field, and temperature on the magnetization behavior, phase diagrams, and hysteresis loops. Very important results were obtained, such as the emergence of first- and second-order phase transitions, multicritical points, zero-temperature highly degenerate points, and multi-loop hysteresis behavior. Hysteresis loops of the graphene monolayer for selected physical parameters [ABSTRACT FROM AUTHOR]

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]