https://doi.org/10.1140/epjb/e2005-00152-1
Specific heat of quantum elastic systems pinned by disorder
1
Theoretische Physik Universität des Saarlandes 66041 Saarbrücken Germany
2
DPMC, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva, Switzerland
3
CNRS-Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 Rue Lhomond 75231
Paris, France
Corresponding author: a schehr@lusi.uni-sb.de
Received:
23
November
2004
Published online:
30
May
2005
We present the detailed study of the thermodynamics of vibrational
modes in disordered elastic systems such as the Bragg glass phase of
lattices pinned by quenched impurities. Our study and our results
are valid within the (mean field) replica Gaussian variational
method. We obtain an expression for the internal energy in the
quantum regime as a function of the saddle point solution, which is
then expanded in powers of 
at low temperature T. In the
calculation of the specific heat Cv a non trivial cancellation of
the term linear in T occurs, explicitly checked to second order in . The final result is 
at low temperatures in dimension three and two. The prefactor is controlled by the
pinning length. This result is discussed in connection with other analytical or numerical studies.
PACS: 75.10.Nr – Spin-glass and other random models / 75.40.Cx – Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.) / 65.60.+a – Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
