Scaling of Low-Temperature Heat Capacity in Cryocrystals

The low-temperature isochoric heat capacity of cryocrystals was scaled using the universal scaling function. This universality links the magnitude of the anomaly and the characteristic temperature of the hump $T_{\mathrm{m}\mathrm{a}\mathrm{x}}$ in heat capacity, which is related to the first van Hove singularity in the phonon spectrum. For atomic, molecular, and quantum cryocrystals, $T_{\mathrm{m}\mathrm{a}\mathrm{x}}$ systematically shifts with molar volume, reflecting Brillouin zone scaling and revealing a common vibrational origin. These findings for the scaling function bridge thermodynamics with the vibrational density of states, highlighting fundamental universality in lattice dynamics.