Europhys. Lett.
Volume 66, Number 4, May 2004
Page(s) 538 - 544
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 May 2004
Europhys. Lett., 66 (4) , pp. 538-544 (2004)
DOI: 10.1209/epl/i2003-10232-x

Specific heat of the quantum Bragg glass

G. Schehr1, T. Giamarchi2 and P. Le Doussal1

1  LPTENS CNRS UMR 8549 - 24 rue Lhomond, 75231 Paris Cedex 05, France
2  DPMC, University of Geneva - 24 quai Ernest-Ansermet CH-1211 Geneva, Switzerland

(Received 28 November 2003; accepted 2 March 2004)

We study the thermodynamics of the vibrational modes of a lattice pinned by impurity disorder in the absence of topological defects (Bragg-glass phase). Using a replica variational method, we compute the specific heat Cv in the quantum regime and find $C_v \propto T^3$ at low temperatures in dimension three and two. The prefactor is controlled by the pinning length. The non-trivial cancellation of the linear term in Cv arises from the so-called marginality condition and has important consequences for other mean-field models.

65.60.+a - Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.
63.50.+x - Vibrational states in disordered systems.
78.55.Qr - Amorphous materials; glasses and other disordered solids.

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