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

TL;DR

This paper introduces a generic coupled block model and renormalization technique to explain the temperature-dependent sound velocity and dielectric constant shifts in glass, aligning well with experimental data and emphasizing long-range interactions.

Contribution

It develops a new coupled block model and renormalization method to explain universal glass susceptibilities, differing from previous tunneling-two-level-system models.

Findings

The model predicts a logarithmic temperature dependence of sound velocity and dielectric constant shifts.

It accurately reproduces the observed slope ratios between relaxation and resonance regimes.

Universal behaviors are attributed to long-range $1/r^3$ interactions, independent of microscopic details.

Abstract

Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $\Delta c/c=\mathcal{C}\ln T$. It does not monotonically increase with temperature from $T=0$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 $\mathcal{C}^{\rm rel }:\mathcal{C}^{\rm res }=-\frac{1}{2}:1$, 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 $\Delta \epsilon/\epsilon=\mathcal{C}\ln T$. 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 $1/r^3$ long range interactions, independent of materials' microscopic properties.