Subloops, Barkhausen noise, and disorder induced critical behavior

Hysteresis loops are often seen in experiments at first order phase transfo rmations when the system goes out of equilibrium, such as in the supercooli ng of liquids and in magnets. The nonequilibrium, zero-temperature random-f ield Ising model has been studied as a model for the hysteretic behavior of these transformations. As disorder is added, one finds a transition where the jump in the saturation hysteresis loop (corresponding to an infinite av alanche) decreases to zero. At this transition the model exhibits power law distributions of noise (avalanches), universal behavior, and a diverging l ength scale [O. Perkovic, K. Dahmen, and J. P. Sethna, Phys. Rev. B 59, 610 6 (1999)]. Interestingly, not only the saturation loops but also subloops r eflect this critical point, and at the critical disorder one finds history- induced critical scaling. We present simulation results for histories in sy stems of almost 14 million spins. Concentric inner subloops are found to re semble rescaled saturation loops at effectively higher (possibly correlated ) disorder. In addition, avalanche size distributions for the inner subloop s are collapsed using Widom scaling methods. The resulting exponents and sc aling functions are shown to differ from those corresponding to the saturat ion loop. (C) 2001 American Institute of Physics.