Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently, Shi {\it et al.} 2008 {\it Phys. Lett.} A {\bf372} 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of earlier work of Tom\'{e} and de Oliveira, 1990 {\it Phys. Rev.} A {\bf41} 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of earlier work of Tom\'{e} and de Oliveira; hence the dynamic phase diagrams calculated by Shi {\it et al.} are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency ($\omega$) and static external field amplitude ($h_{0})$ for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on values of $\omega$ and $h_{0}$.