Goldstone fluctuations in the amorphous solid stateS. Mukhopadhyay1, P. M. Goldbart1 and A. Zippelius2
1 Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, IL 61801-3080, USA
2 Institut für Theoretische Physik, Georg-August-Universität Göttingen 37073 Göttingen, Germany
(Received 28 October 2003; accepted 29 April 2004)
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.
61.43.-j - Disordered solids.
82.70.Gg - Gels and sols.
© EDP Sciences 2004