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We have used the Curie–Weiss mean-field approximation to study the effects of the random single-ion anisotropy and random magnetic field in the phase diagram and thermodynamic properties of the spin-5/2 Blume–Capel model. The phase diagrams have been presented in the temperature T ∕ J versus strength random single-ion anisotropy D ∕ J and strength random magnetic field h ∕ J planes. The magnetization dependence was plotted as a function of temperature and the strength single-ion anisotropy. These diagrams showed that the different phase transition types, first-or second-order between the ferromagnetic and paramagnetic phases, are dependent on the random parameters. Therefore, within these conditions, the model presents tricritical behavior. • Several phase diagrams were obtained for the spin-5/2 Blume–Capel model. • The influence of the random single-ion anisotropy and magnetic field was examined for the system. • First- and second-order phase transition lines were found. • The tricritical behavior was examined. [ABSTRACT FROM AUTHOR]

Abstract 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 = k B T ∕ z J versus single-ion anisotropy δ x = D x ∕ z J plane for several values of δ y = D y ∕ z J , p and q. The results show that there is a tricritical behavior only in the range of δ y given by − 0. 048 ≤ δ y < 0. 5. This behavior is shown again by the curves of the magnetization m as a function of temperature τ with corresponding values of δ y , p and q. Highlights • Several phase diagrams were obtained for the spin-1 Blume–Capel quantum model. • The influence of the random single-ion anisotropies was examined for the system. • First- and second-order phase transition lines were found. • The tricritical behavior was examined. [ABSTRACT FROM AUTHOR]

We have studied the effects of the random single-ion anisotropy and random magnetic field in the phase diagram and in the thermodynamic properties of the spin-3/2 Blume–Capel model via Curie–Weiss mean-field approximation. The phase diagrams were built in the planes temperature versus single-ion anisotropy, temperature versus magnetic field, temperature versus random parameters and the dependencies of magnetization were plotted versus temperature and single-ion anisotropy. These diagrams show that, in the space ( D / J − T / J ) , the type (first- or second-order) of the phase transition between the ferromagnetic and paramagnetic phases is dependent on the random parameters. Therefore, within these conditions the model presents tricritical behavior. For large values, and a certain critical value of the random parameters, the phase transition is only of second-order, but it is of first-order within the ordered phase, between the phase with m = 1 / 2 and m = 3 / 2 , which ends in a terminal critical point. [ABSTRACT FROM AUTHOR]