Anomalous Sound Velocity and Dielectric Shift in Glass: a Renormalization Technique for Mechanical and Dielectric Susceptibilities from Generic Coupled Block Model

Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $\Delta c/c=$\mathcal{C}$\ln T$\mathrm{.}Itdoesnotmonotonicallyincreasewithtemperaturefrom$T=0$K, but to reach a maximum around a few Kelvin. Different from tunneling-two-level-system (TTLS) which gives the slope ratio between relaxation and resonance regimes ${\mathcal{C}}^{\mathrm{r}\mathrm{e}\mathrm{l}}:{\mathcal{C}}^{\mathrm{r}\mathrm{e}\mathrm{s}}=-\frac{1}{2}:1$, we develop a generic coupled block model to give $$\mathcal{C}$^{\rm rel }:$\mathcal{C}$^{\rm res }=-1:1$, which agrees well with the majority of experimental measurements. We use electric dipole-dipole interaction to carry out a similar behavior for glass dielectric constant shift $\mathrm{\Delta }ϵ\mathrm{/}ϵ=\mathcal{C}\ln T$. The slope ratio between relaxation and resonance regimes is $$\mathcal{C}$^{\rm rel}:$\mathcal{C}$^{\rm res}=1:-1$ which agrees with dielectric measurements quite well. By developing a renormalization procedure for non-elastic stress-stress and dielectric susceptibilities, we prove these universalities essentially come from $1\mathrm{/}{r}^3$ long range interactions, independent of materials’ microscopic properties.