The van Hemmen model and effect of random crystalline anisotropy field

•Several phase diagrams are obtained for the model.•The influence of the random crystalline anisotropy field on the model is investigated.•Three ordered (spin-glass, ferromagnetic and mixed) phases are found.•The tricritical behavior is examined.

In this work, we have presented the generalized phase diagrams of the van Hemmen model for spin S=1 in the presence of an anisotropic term of random crystalline field. In order to study the critical behavior of the phase transitions, we employed a mean-field Curie–Weiss approach, which allows calculation of the free energy and the equations of state of the model. The phase diagrams obtained here displayed tricritical behavior, with second-order phase transition lines separated from the first-order phase transition lines by a tricritical point.