Hierarchical Jamming


The free energy landscape of mean-field marginal glasses is ultrametric. We demonstrate that this feature persists in finite three-dimensional systems that are out of equilibrium by finding sets of minima, which are nearby in configuration space. By calculating the distance between these nearby minima, we produce a small region of the distance metric. This metric exhibits a clear hierarchical structure and shows the signature of an ultrametric space. That such a hierarchy exists for the jamming energy landscape provides direct evidence for the existence of a marginal phase along the zero temperature jamming line.

Jamming Energy Landscape is Hierarchical and Ultrametric