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 by Marchetti et al. [Phys. Rev. Lett. 85, 1104 (2000)], the model appears to be in the same universality class as the zero-temperature random field Ising model of hysteresis in magnets.