Goldstone fluctuations in the amorphous solid state

TL;DR

This paper investigates Goldstone modes in amorphous solids, showing how spontaneous symmetry breaking leads to shear excitations that influence localization, especially in two dimensions where fluctuations destroy true localization.

Contribution

It identifies the broken symmetry as relative translations of replicas and constructs Goldstone excitations from long wavelength distortions, providing a microscopic understanding of amorphous solid elasticity.

Findings

Goldstone fluctuations destroy localization in 2D amorphous solids.

Elastic free energy is explicitly computed from a microscopic model.

Power-law correlations characterize the 2D amorphous solid state.

Abstract

Goldstone modes in the amorphous solid state, resulting from the spontaneous breaking of translational symmetry due to random localisation of particles, are discussed. Starting from a microscopic model with quenched disorder, the broken symmetry is identified to be that of relative translations of the replicas. Goldstone excitations, corresponding to pure shear deformations, are constructed from long wavelength distortions of the order parameter. The elastic free energy is computed, and it is shown that Goldstone fluctuations destroy localisation in two spatial dimensions, yielding a two-dimensional amorphous solid state characterised by power-law correlations.