±J Blume-Capel model in the cluster variation method

The ± J Blume-Capel model is studied by using the cluster variation method (CVM) in its first approximation which yields results equal to the mean-field ones. The spins are assumed to be interacting either ferromagnetically or antiferromagnetically with the given probabilities p or 1−p, respectively. The phase diagrams of the model are obtained on the temperature (T)-probability (p) or crystal field (D) planes for given D and p, respectively. The model is examined by introducing the dipolar and quadrupolar order-parameters and, ferromagnetic (F), antiferromagnetic (AF) and paramagnetic (P) phase regions are explored. It is found that the model gives first- and second-order phase transitions and tricritical points.