Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, $$B_{\mathrm {c}}$$ B c and $$d_{\mathrm {c}}$$ d c , the relaxation time $$\tau $$ τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, $$\tau (d)$$ τ ( d ) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, $$\tau (d)$$ τ ( d ) exhibits a power-law divergence at the same $$d_{\mathrm {c}}$$ d c with nearly the same exponent.

When many-particle (vortex) assemblies with disordered distribution are subjected to a periodic shear with a small amplitude , the particles gradually self-organize to avoid next collisions and transform into an organized configuration. We can detect it from the time-dependent voltage (average velocity) that increases towards a steady-state value. For small , 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 above a threshold . 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 . By measuring , 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 to reach either the reversible or irreversible state shows a power-law divergence at . 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 is decreased down to the intervortex spacing in the reversible regime, 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.

We study the critical dynamics of vortices associated with dynamic disordering near the depinning transitions driven by dc force (dc current I) and vortex density (magnetic field B). Independent of the driving parameters, I and B, we observe the critical behavior of the depinning transitions, not only on the moving side, but also on the pinned side of the transition, which is the first convincing verification of the theoretical prediction. Relaxation times, $$\tau (I)$$ τ ( I ) and $$\tau (B)$$ τ ( B ) , to reach either the moving or pinned state, plotted against I and B, respectively, exhibit a power-law divergence at the depinning thresholds. The critical exponents of both transitions are, within errors, identical to each other, which are in agreement with the values expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. With an increase in B under constant I, the depinning transition at low B is replaced by the repinning transition at high B in the peak-effect regime. We find a trend that the critical exponents in the peak-effect regime are slightly smaller than those in the low-B regime and the theoretical one, which is attributed to the slight difference in the depinning mechanism in the peak-effect regime.

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