Discontinuous scaling of hysteresis losses

We study the dependence of hysteresis loop area A on the frequency Ω and amplitude H of the driving field for several mean-field treatments of the kinetic Ising model. An unusual discontinuous double-power-law scaling behavior is found in all cases. In the low-frequency regime, it is found that A-${\mathit{A}}_0$∼${\mathit{H}}^{2/3}$ ${\mathrm{\Omega }}^{2/3}$ ${\mathit{scrG}}_{\mathit{L}}$(Ω/${\mathit{H}}^{\gamma }$), where ${\mathit{A}}_0$ is the zero-frequency value of the loop area, ${\mathit{scrG}}_{\mathit{L}}$ is a scaling function, and γ is a model-dependent exponent. In the high-frequency regime, the loop area itself scales with frequency and amplitude as A∼${\mathit{H}}^{\mathrm{\alpha }}$ ${\mathrm{\Omega }}^{\mathrm{-}1}$, where α is also a model-dependent exponent. The transition between these extremes is sharp and can be characterized by an amplitude-dependent critical frequency. We also note differences in behavior above and below the critical ordering temperature ${\mathit{T}}_{\mathit{C}}$.