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.
Infinitely-many absorbing-state nonequilibrium phase transitions
