A glass-like behavior in the low-temperature specific heat is a natural property of any real crystal

TL;DR

This paper demonstrates that real crystals exhibit glass-like low-temperature specific heat due to defects, with a calculated free energy leading to a linear temperature dependence similar to glasses, challenging the notion that perfect crystal spectra determine low-temperature behavior.

Contribution

It provides a rigorous calculation showing that defects induce glass-like low-temperature specific heat in crystals, highlighting the importance of imperfections.

Findings

Low-temperature free energy scales as T^2

Specific heat is linear in T at low temperatures

Defects cause glass-like behavior in crystals

Abstract

We provide a rigorous calculation of the free energy of a non-metallic crystal containing a small concentration of defects. The low-temperature leading contribution is found to be $\propto T^2$. This further gives a linear-in-$T$ low-temperature specific heat as that exhibited by glasses. These results also show that, similarly to what happens in glasses, the long-wavelength spectrum of a nearly perfect crystal does not suffice to determine its low-temperature behavior.