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 kineticIsing model in the presence of a sinusoidal oscillating field andpresented the dynamic phase diagrams by using an effective-fieldtheory (EFT) and a mean-field theory (MFT). The MFT results are inconflict with those of earlier work of Tom'{e} and de Oliveira,[1990 {it Phys. Rev.} A {bf41} 4251]. We calculate the dynamicphase diagrams and find that our results are similar to those ofearlier work of Tom'{e} and de Oliveira; hence the dynamic phasediagrams calculated by Shi {it et al.} are incomplete within boththeories, except the low values of frequencies for the MFTcalculation. We also investigate the influence of external fieldfrequency ($omega$) and static external field amplitude ($h_{0})$for both MFT and EFT calculations. We find that the behaviour of thesystem strongly depends on values of $omega$ and $h_{0}$.