Subloops, Barkhausen noise, and disorder induced critical behavior

Hysteresis loops are often seen in experiments at first order phase transformations when the system goes out of equilibrium, such as in the supercooling of liquids and in magnets. The nonequilibrium, zero-temperature random-field 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 avalanche) decreases to zero. At this transition the model exhibits power law distributions of noise (avalanches), universal behavior, and a diverging length scale [O. Perković, K. Dahmen, and J. P. Sethna, Phys. Rev. B 59, 6106 (1999)]. Interestingly, not only the saturation loops but also subloops reflect this critical point, and at the critical disorder one finds history-induced critical scaling. We present simulation results for histories in systems of almost 14 million spins. Concentric inner subloops are found to resemble rescaled saturation loops at effectively higher (possibly correlated) disorder. In addition, avalanche size distributions for the inner subloops are collapsed using Widom scaling methods. The resulting exponents and scaling functions are shown to differ from those corresponding to the saturation loop.