Scaling on hysteresis in a model spin system

Abstract

The dynamic hysteresis in a model continuum spin system is studied by statistical–mechanical approach based on the three-dimensional ( Φ 2) 2 model with O( N) symmetry in the limit N→∞. The dependence of the hysteresis area A on the frequency f and the amplitude H 0 of the externally applied field is investigated in detail. The single-peak pattern A( f) at fixed H 0 is revealed over a wide range of H 0. A scaling relationship is proposed for the hysteresis area spectrum A( f, H 0) in which a scaling function W( η)∝ τ 1 A( f, H 0), where η=log( fτ 1) and τ 1 is the unique characteristic time for the spin reverse, applies to all A( f, H 0), unless H 0 is very small. The inverse characteristic time τ 1 −1 shows a perfect linear dependence on the amplitude H 0, supported by the well-established experimental evidence.