We study the zero temperature properties of hysteresis in a site-diluted Ising model. The model exhibits a critical line separating a disordered from an incipient ferromagnetic ground state: the shape of the hysteresis loop changes from a smooth cycle (formed as a sequence of tiny avalanches) to a sharp cycle exhibiting a macroscopic reversal of the magnetization for a given value of the field (infinite avalanche). Criticality is characterized by power-law distribution of avalanche sizes. Model predictions are contrasted with experimental results obtained in Cu–Al–Mn alloys.