Study of thermal and magnetic properties of the blume-capel model with the correlated effective field method

The temperature dependences of the magnetization and quadrupolar moment order parameters of the Blume-Capel model with bilinear (J) and single-ion anisotropy (D) parameter is studied by using the correlated effective field method. It is assumed that the external magnetic field is zero. Beside the stable solutions, metastable or unstable states of the order parameters are also found for the various values of parameters. In this system, the phase transition depends on the single-ion anisotropy parameters, therefore the dependence of the nature of the phase transition is investigated extensively.The low-temperature magnetization plateaus of the model in an external magnetic field and single-ion anisotropy are also investigated by using the cluster variation method and restricting ourselves to the case of antiferromagnetic exchange interactions. Low-temperature magnetization curves show step-like plateau characterized by several critical magnetic fields. The effects of the external magnetic field and single-ion anisotropy parameters on the magnetization plateaus are discussed in detail.