Response of Ising systems to oscillating and pulsed fields: Hysteresis, ac, and pulse susceptibility

We have studied, using Monte Carlo (MC) simulation for ferromagnetic Ising systems in one to four dimensions and solving numerically the mean-field (MF) equation of motion, the nature of the response magnetization m(t) of an Ising system in the presence of a periodically varying external field [h(t)=${\mathit{h}}_0$cos(ωt)]. From these studies, we determine the m-h loop or hysteresis loop area A(=∮mdh) and the dynamic order parameter Q(=∮mdt) and investigate their variations with the frequency (ω) and amplitude (${\mathit{h}}_0$) of the applied external magnetic field and the temperature (T) of the system. The variations in A are fitted to a scaling form, assumed to be valid over a wide range of parameter (ω,${\mathit{h}}_0$,T) values, and the best-fit exponents are obtained in all three dimensions (D=2,3,4). The scaling function is Lorentzian in the MF case and is exponentially decaying, with an initial power law, for the MC cases. The dynamic phase boundary (in the ${\mathit{h}}_0$-T plane) is found to be frequency dependent and the transition (from Q≠0 for low T and ${\mathit{h}}_0$ to Q=0 for high T and ${\mathit{h}}_0$) across the boundary crosses over from a discontinuous to a continuous one at a tricritical point. These boundaries are determined in various cases.