Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, $f(t)=f_0\exp [-(t\mathrm{/}\tau {)}^{\beta }]$, with the exponent $\beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $T\to 0$. A relation between the specific heat and the entropy in the long time regime is found.