  In low-temperature glasses, the sound velocity changes as the logarithmic
function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) =
\mathcal{C}\ln(T/T_0)$. With increasing temperature starting from $T=0$K, the
sound velocity does not increase monotonically, but reaches a maximum at a few
Kelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS)
model explained the $\ln T$ dependence of sound velocity shift. In TTLS model
the slope ratio of $\ln T$ dependence of sound velocity shift between lower
temperature increasing regime (resonance regime) and higher temperature
decreasing regime (relaxation regime) is $\mathcal{C}^{\rm res
}:\mathcal{C}^{\rm rel }=1:-\frac{1}{2}$. In this paper we develop the generic
coupled block model to prove the slope ratio of sound velocity shift between
two regimes is $\mathcal{C}^{\rm res }:\mathcal{C}^{\rm rel }=1:-1$ rather than
$1:-\frac{1}{2}$, which agrees with the majority of the measurements. The
dielectric constant shift in low-temperature glasses,
$[\epsilon_r(T)-\epsilon_r(T_0)]/\epsilon_r(T_0)$, has a similar logarithmic
temperature dependence below $10$K: $[\epsilon(T)-\epsilon(T_0)]/\epsilon(T_0)
= \mathcal{C}\ln(T/T_0)$. In TTLS model the slope ratio of dielectric constant
shift between resonance and relaxation regimes is $\mathcal{C}^{\rm
res}:\mathcal{C}^{\rm rel}=-1:\frac{1}{2}$. In this paper we apply the electric
dipole-dipole interaction, to prove that the slope ratio between two regimes is
$\mathcal{C}^{\rm res}:\mathcal{C}^{\rm rel} = -1:1$ rather than
$-1:\frac{1}{2}$. Our result agrees with the dielectric constant measurements.
By developing a real space renormalization technique for glass non-elastic and
dielectric susceptibilities, we show that these universal properties
essentially come from the $1/r^3$ long range interactions, independent of the
materials' microscopic properties.
