Critical behavior of density-driven and shear-driven reversible–irreversible transitions in cyclically sheared vortices

Abstract

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.

Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

“…The relative width of the critical region, , , and , which spans the broad range up to near 1, is also nearly independent of the driving parameters. The feature is very similar to that observed recently in the shear-driven and density-driven RIT in the cyclically sheared vortices 26 . However, we find a trend that the critical exponents 1.0 in the peak-effect regime are slightly smaller than 1.3 in the low- B region and than expected for the 2D DP class, whose origin is attributed to the slight difference in the depinning mechanism in the peak-effect regime.…”

“…The observed independence of the critical exponents from the driving parameters is somewhat surprising, considering that the critical regions observed here are very large, clearly going beyond the linear approximation. The similar large critical region has been reported in the nonequilibrium RIT in various systems 17 , 22 , 25 , including the vortex system 24 , where the parameter-independent critical exponents with 1.3–1.4 have been found for the shear-driven and density-driven transitions 26 .…”

“…This is an interesting problem to be solved in future research. It is also of interest to note that the asymmetry in about the transition is observed in different physical systems that exhibit RIT 17 , 26 , which would fall into the same universal class as the depinning transition and the absorbing transition in DP.

Figure 5 The relative width of the critical region.

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“…Many-particle systems subjected to an external driving force exhibit a variety of nonequilibrium phases and phase transitions, such as a plastic depinning transition 1 – 14 and a reversible-irreversible transition (RIT) 15 – 26 . The depinning phenomenon of collectively interacting particle systems driven over random substrates has been observed ubiquitously 13 in various physical systems 6 – 14 , 27 – 29 , including sliding charge density waves 30 , Wigner crystals 31 , 32 , colloids 3 , 33 , magnetic domain walls 34 , and superconducting vortices in type-II superconductors 1 , 2 , 4 , 5 , 35 .…”

“…In these experiments, however, the critical behavior of the depinning transition has been observed only on the moving (fluctuating diffusing [active]) side of the transition 9 , 12 , 20 , 39 , although that of RIT has been reported on both sides of the transition 20 , 24 , 26 . This is because it is difficult to obtain a reliable data of V ( t ) in the pinned (non-fluctuating quiescent [absorbing]) phase, where V ( t ) relaxes to = 0.…”