Critical behavior near the reversible-irreversible transition in periodically driven vortices under random local shear

Abstract

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