Document Europhys. Lett., 67 (1) , pp. 49-55 (2004)
DOI: 10.1209/epl/i2003-10278-8
Goldstone fluctuations in the amorphous solid state
S. Mukhopadhyay1, P. M. Goldbart1 and A. Zippelius21 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)
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.
61.43.-j - Disordered solids.
82.70.Gg - Gels and sols.
© EDP Sciences 2004