Europhys. Lett.
Volume 67, Number 1, July 2004
Page(s) 49 - 55
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 June 2004
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. 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