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In low-temperature glasses, the sound velocity changes as the logarithmicfunction 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, thesound velocity does not increase monotonically, but reaches a maximum at a fewKelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS)model explained the $\ln T$ dependence of sound velocity shift. In TTLS modelthe slope ratio of $\ln T$ dependence of sound velocity shift between lowertemperature increasing regime (resonance regime) and higher temperaturedecreasing regime (relaxation regime) is $\mathcal{C}^{\rm res}:\mathcal{C}^{\rm rel }=1:-\frac{1}{2}$. In this paper we develop the genericcoupled block model to prove the slope ratio of sound velocity shift betweentwo 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. Thedielectric constant shift in low-temperature glasses,$[\epsilon_r(T)-\epsilon_r(T_0)]/\epsilon_r(T_0)$, has a similar logarithmictemperature 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 constantshift between resonance and relaxation regimes is $\mathcal{C}^{\rmres}:\mathcal{C}^{\rm rel}=-1:\frac{1}{2}$. In this paper we apply the electricdipole-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 anddielectric susceptibilities, we show that these universal propertiesessentially come from the $1/r^3$ long range interactions, independent of thematerials' microscopic properties.

A Microscopic Field Theory for the Universal Shift of Sound Velocity and Dielectric Constant in Low-Temperature Glasses