Jamming Energy Landscape is Hierarchical and Ultrametric

TL;DR

This paper demonstrates that the hierarchical and ultrametric nature of the free energy landscape in mean field marginal glasses persists in finite three-dimensional systems, providing evidence for a marginal phase at jamming.

Contribution

It shows that the ultrametric structure of the energy landscape extends from mean field models to finite-dimensional systems, revealing a hierarchical organization in the jamming landscape.

Findings

The energy landscape exhibits a hierarchical structure.

The distance metric between minima is ultrametric.

Evidence supports a marginal phase at jamming.

Abstract

The free energy landscape of mean field marginal glasses is ultrametric. We demonstrate that this feature remains in finite three dimensional systems 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.