Abstract
When many-particle (vortex) assemblies with disordered distribution are subjected to a periodic shear with a small amplitude [Formula: see text], the particles gradually self-organize to avoid next collisions and transform into an organized configuration. We can detect it from the time-dependent voltage [Formula: see text] (average velocity) that increases towards a steady-state value. For small [Formula: see text], the particles settle into a reversible state where all the particles return to their initial position after each shear cycle, while they reach an irreversible state for [Formula: see text] above a threshold [Formula: see text]. Here, we investigate the general phenomenon of a reversible-irreversible transition (RIT) using periodically driven vortices in a strip-shaped amorphous film with random pinning that causes local shear, as a function of [Formula: see text]. By measuring [Formula: see text], we observe a critical behavior of RIT, not only on the irreversible side, but also on the reversible side of the transition, which is the first under random local shear. The relaxation time [Formula: see text] to reach either the reversible or irreversible state shows a power-law divergence at [Formula: see text]. The critical exponent is determined with higher accuracy and is, within errors, in agreement with the value expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. As [Formula: see text] is decreased down to the intervortex spacing in the reversible regime, [Formula: see text] deviates downward from the power-law relation, reflecting the suppression of intervortex collisions. We also suggest the possibility of a narrow smectic-flow regime, which is predicted to intervene between fully reversible and irreversible flow.