When random assemblies of particles are cyclically sheared with a shear amplitude d, collisions between the particles cause the system to self-organize into a relatively ordered configuration where less collisions occur.For a small shear amplitude d, the particles finally 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 d above a threshold amplitude d_c [1]. Using cyclically sheared vortices in amorphous Mo_xGe_1-x films with random pinning, we have demonstrated the critical behavior of the reversible-irreversible transition (RIT). The relaxation time τ(d) to reach the steady state shows a power-law divergence at d_c, indicative of a nonequilibrium RIT [2,3]. The critical exponent agrees with the value expected for an absorbing phase transition in the two-dimensional directed-percolation universality class [4]. Recently, we have found that, when d is decreased to the average intervortex spacing in the reversible regime, τ(d) shows a significant drop, reflecting the suppression of vortex-vortex collisions [3]. This indicates a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state [5]. Here, we perform a detailed analysis of τ(d) in the reversible states and find that, in either regime, τ(d) exhibits a power-law divergence at the same d_c with nearly the same exponent [6].

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[2] S. Okuma, Y. Tsugawa, and A. Motohashi, Phys. Rev. B 83, 012503 (2011): M. Dobroka et al., New J. Phys. 19, 053023 (2017).
[3] S. Maegochi, K. Ienaga, S. Kaneko, and S. Okuma, Sci. Rep. 9, 16447 (2019).
[4] H. Hinrichsen, Adv. Phys. 49, 815 (2000).
[5] P. Das, H. A. Vinutha, and S. Sastry, Proc. Natl. Acad. Sci. USA 117, 10203 (2020).
[6] S. Maegochi, K. Ienaga, and S. Okuma, preprint.

Keywords: nonequilibrium transition, reversible-irreversible transition, absorbing phase transition