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.