Minimal cyclic behavior in sheared amorphous solids

Although jammed packings of soft spheres exist in potential-energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle rearrangements are represented by spin flips, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings. We select pairs of rearrangements that undo one another to create periodic cyclic behavior, explore the statistics of these pairs, and show that their internal structure is more complex than a spin analogy would indicate. This offers insight into both the collective nature of rearrangement events themselves and how complex systems such as amorphous solids can reach a limit cycle with relative ease.