Scaling on hysteresis in a model spin system

The dynamic hysteresis in a model continuum spin system is studied by stati stical-mechanical approach based on the three-dimensional (Phi (2))(2) mode l with O(N) symmetry in the limit N --> infinity. The dependence of the hys teresis area A on the frequency f and the amplitude H-o of the externally a pplied-field is investigated in detail. The single-peak pattern A(f) at fix ed H-o is revealed over a wide range of H-o. A scaling relationship is prop osed for the hysteresis area spectrum A(f,H-o) in which a scaling function W(eta) proportional to tau (1)A(f,H-o), where eta = log(f tau (1)) and tau (1) is the unique characteristic time for the spin reverse, applies to all A(f,H-o), unless H-o is very small. The inverse characteristic time tau (-1 )(1) shows a perfect linear dependence on the amplitude H-o, supported by t he well-established experimental evidence. (C) 2001 Elsevier Science Ltd. A ll rights reserved.