Hysteresis in driven disordered systems: From plastic depinning to magnets

We study the dynamics of a viscoelastic medium driven through quenched disorder by expanding about mean field theory in $6-\epsilon$ dimensions. The model exhibits a critical point separating a region where the dynamics is hysteretic with a macroscopic jump between strongly pinned and weakly pinned states, from a region where the sliding state is unique and no jump occurs. The disappearance of the jump at the critical point is described by universal exponents. As suggested in \onlinecite{MMP00}, the model appears to be in the same universality class as the zero-temperature random field Ising model of hysteresis in magnets.