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-A₀{~}H2/3{{{Ω}}}2/3scrGL({Ω}/H^γ), where A₀ is the zero-frequency value of the loop area, scrGL 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{~}H^α{{{Ω}}}^{{{-}}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 TC.