Field theory for amorphous solids

TL;DR

This paper develops a field theory for amorphous solids that explains long-range stress correlations as a consequence of mechanical equilibrium, providing explicit predictions and new insights into the structure of glasses.

Contribution

It introduces a novel field theoretical framework for inherent states in amorphous solids, linking stress correlations to mechanical equilibrium and deriving equations of state.

Findings

Stress correlations follow from mechanical equilibrium.

Explicit predictions for 2D and 3D stress correlations.

Identification of a new holographic quantity in 3D systems.

Abstract

Glasses at low temperature fluctuate around their inherent states; glassy anomalies reflect the structure of these states. Recently there have been numerous observations of long-range stress correlations in glassy materials, from supercooled liquids to colloids and granular materials, but without a common explanation. Herein it is shown, using a field theory of inherent states, that long-range stress correlations follow from mechanical equilibrium alone, with explicit predictions for stress correlations in 2 and 3 dimensions. `Equations of state' relating fluctuations to imposed stresses are derived, as well as field equations that fix the spatial structure of stresses in arbitrary geometries. Finally, a new holographic quantity in 3D amorphous systems is identified.