Goldstone fluctuations in the 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.

7 pages, 2 figures

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Cited by in corpus (8)

• Glass elasticity from particle trajectories
• Emergence of long-ranged stress correlations at the liquid to glass transition
• Soft random solids and their heterogeneous elasticity
• Random networks of cross-linked directed polymers
• Goldstone-type fluctuations and their implications for the amorphous solid state
• Elastic heterogeneity of soft random solids
• Dynamics of gelling liquids: a short survey
• Cavity Approach to the Random Solid State