Hysteresis and avalanches: Phase transitions and critical phenomena in driven disordered systems

We discuss Barkhausen noise in magnetic systems in terms of avalanches near a disorder-induced critical point, using the hysteretic zero-temperature random-field Ising model and recent variants. As the disorder is decreased, one finds a transition from smooth hysteresis loops to loops with a sharp jump in magnetization (corresponding to an infinite avalanche). In a large region near the transition point the model exhibits power-law distributions of noise (avalanches), universal behavior and a diverging length scale. Universal properties of this critical point are reported that were obtained using renormalization group methods and numerical simulations. Connections to other experimental systems such as athermal martensitic phase transitions (with and without 'bursts') and front propagation are also discussed.