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 interacting spin flips called hysterons, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects and how such objects interact with one another. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings and select pairs of rearrangements that undo one another to create periodic cyclic behavior. We find that the rearrangement pairs surprisingly persist down to the smallest increments in strain, even in the smallest systems we can study. We explore the statistics of these rearrangement pairs and find that there is a relation between the amount of hysteresis and the energy drop and mean-square displacement of the particles; these results are inconsistent with the scaling found in models that treat rearrangements as localized buckling events. Finally, our analysis shows that there is no clean distinction between the "core" of an individual rearrangement and the interactions between rearrangements. These results offer insight into how complex systems such as amorphous solids can reach a limit cycle.