LAUSR

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 .