Hysteresis in an ising chain with quenched random disorder

A probabilistic method is used to obtain an exact analytic expression for the zero-temperature and zero-frequency limit of the hysteresis loop in a one-dimensional Ising model with an arbitrary continuous distribution of quenched random fields. The solution illustrates important differences between bounded and unbounded probability distributions of the quenched fields. The significance of this result is discussed in the wider context of the Barkhausen noise observed in experiments as well as numerical simulations of three-dimensional systems.