Effective-field theory on the transverse Ising model under a time oscillating longitudinal field

As an analytical method, the effective-field theory (EFT) is used to study an Ising spin system in a transverse magnetic field under a time oscillating longitudinal field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4Z=4). In the longitudinal field amplitude h0/ZJh0/ZJ-transverse field Γ/ZJΓ/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase also has been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The dependence of the critical temperature on the transverse field is calculated and phase diagrams are presented. We also make the compare results of EFT with that given by using the mean field theory (MFT).