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Jamming Energy Landscape is Hierarchical and Ultrametric.

R C Dennis1, E I Corwin1

  • 1Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA.

Physical Review Letters
|March 7, 2020
PubMed
Summary

The ultrametric structure of mean-field marginal glasses persists in finite 3D systems. This hierarchical organization in the jamming energy landscape provides evidence for a marginal phase.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Mean-field models suggest ultrametric free energy landscapes for marginal glasses.
  • Ultrametricity implies a hierarchical organization of states in configuration space.
  • Understanding these landscapes is crucial for explaining glass properties.

Purpose of the Study:

  • To investigate if the ultrametric property of mean-field marginal glasses extends to finite, non-equilibrium 3D systems.
  • To provide evidence for the existence of a marginal phase in jamming phenomena.

Main Methods:

  • Identifying sets of nearby minima in the configuration space of finite 3D systems.
  • Calculating the distance metric between these nearby minima.
  • Analyzing the hierarchical structure of the resulting distance metric.

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Main Results:

  • Demonstrated that the distance metric between nearby minima exhibits a clear hierarchical structure.
  • Confirmed the signature of an ultrametric space in finite 3D systems.
  • Established a link between this hierarchy and the jamming energy landscape.

Conclusions:

  • The ultrametric feature of the free energy landscape is not limited to mean-field models but extends to finite 3D systems.
  • The observed hierarchical structure in the jamming energy landscape provides direct evidence for a marginal phase.
  • This finding deepens our understanding of the nature of glasses and jamming transitions.