Specific Heat of Quantum Elastic Systems Pinned by Disorder

Details Specific Heat of Quantum Elastic Systems Pinned by Disorder Specific Heat of Quantum Elastic Systems Pinned by Disorder

2004-11-09

arxiv.org/abs/cond-mat/0411227v1

Eur. Phys. J. B 44 (2005), 521

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages

Scientific paper

10.1140/epjb/e2005-00152-1

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 $\hbar$ at low temperature $T$. In the calculation of the specific heat $C_v$ a non trivial cancellation of the term linear in $T$ occurs, explicitly checked to second order in $\hbar$. The final result is $C_v \propto T^3$ 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.

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