Jamming Energy Landscape is Hierarchical and Ultrametric

Physical Review Letters
R C Dennis, Eric I Corwin

Abstract

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.

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Citations

Feb 13, 2021·Physical Review Letters·James D SartorEric I Corwin
Jan 30, 2021·Physical Review Letters·Samuel AlbertPierfrancesco Urbani

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