Effective-field theory on the kinetic spin-1 Blume–Capel model

The effective-field theory (EFT) is used to study the dynamical response of the kinetic spin-1 Blume–Capel model in the presence of a sinusoidal oscillating magnetic field. The effective-field dynamic equations are given for the honeycomb lattice ( Z = 3 ) . The dynamic order parameter, the dynamic quadruple moment, the hysteresis loop area and the dynamic correlation are calculated. We have found that the behavior of the system strongly depends on the crystal interaction D . The dynamic phase boundaries separating the paramagnetic phase and the ferromagnetic phase are obtained. There is the region of the phase space where both a paramagnetic phase and a ferromagnetic phase coexist. The dynamic transition from one region to the other can be of first or second order depending on the frequency of the magnetic field. There is no dynamic tricritical point on the dynamic phase transition line. The results are also compared with those obtained from the mean-field theory (MFT).