Field theory for amorphous solids
arXiv:1808.01811 · doi:10.1103/PhysRevLett.121.118001
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.
5 pages. Short version to appear in PRL. Extended version available at arXiv:1804.04834
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- Emergent Elasticity in Amorphous Solids
- Connecting shear localization with the long-range correlated polarized stress fields in granular materials
- Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory
- Protocol-Dependence and State Variables in the Force-Moment Ensemble
- Effect of pinning on the yielding transition of amorphous solids
- Stress-stress Correlations Reveal Force Chains in Gels
- Tensor Electromagnetism and Emergent Elasticity in Jammed Solids
- Edwards field theory for glasses and granular matter
- Schramm-Loewner evolution in 2d rigidity percolation
- Evidences of conformal invariance in 2d rigidity percolation
- Renormalization of elastic quadrupoles in amorphous solids
- Random quench predicts universal properties of amorphous solids
- Long-range correlations in pinned athermal networks
- Note: Simple argument for emergent anisotropic stress correlations in disordered solids
- Displacement correlations in disordered athermal networks
- Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition
- Stress-stress correlations in two-dimensional amorphous and crystalline solids