Scaling on hysteresis in a model spin system

The dynamic hysteresis in a model continuum spin system is studied by statistical–mechanical approach based on the three-dimensional (Φ2)2 model with O(N) symmetry in the limit N→∞. The dependence of the hysteresis area A on the frequency f and the amplitude H0 of the externally applied field is investigated in detail. The single-peak pattern A(f) at fixed H0 is revealed over a wide range of H0. A scaling relationship is proposed for the hysteresis area spectrum A(f,H0) in which a scaling function W(η)∝τ1A(f,H0), where η=log(fτ1) and τ1 is the unique characteristic time for the spin reverse, applies to all A(f,H0), unless H0 is very small. The inverse characteristic time τ1−1 shows a perfect linear dependence on the amplitude H0, supported by the well-established experimental evidence.