The quasi-low temperature behaviour of specific heat

TL;DR

This paper introduces a scale-free, finite temperature field theory approach to condensed matter physics, predicting a universal quartic temperature dependence of specific heat at low temperatures, supported by experimental data across various materials.

Contribution

It proposes a new mathematical formalism based on dimensionless variables that explains the quasi-low temperature behavior of specific heat in diverse condensed matter systems.

Findings

Specific heat follows a quartic temperature law in the quasi-low temperature regime.

The quartic law is supported by experimental data for various lattice and glassy materials.

The study links the 'boson peak' temperature to shear velocity, providing new insights into lattice dynamics.

Abstract

A new mathematical approach to condensed matter physics, based on the finite temperature field theory, was recently proposed. The field theory is a scale-free formalism, thus, it denies absolute values of thermodynamic temperature and uses dimensionless thermal variables, which are obtained with the group velocities of sound and the interatomic distance. This formalism was previously applied to the specific heat of condensed matter and predicted its fourth power of temperature behaviour at sufficiently low temperatures, which was tested by experimental data for diamond lattice materials. The range of temperatures with the quartic law varies for different materials, therefore, it is called the quasi-low temperature regime. The quasi-low temperature behavior of specific heat is verified here with experimental data for the fcc lattice materials, silver chloride and lithium iodide. The conjecture that the fourth order behavior is universal for all condensed matter systems is also supported the data for glassy matter: vitreous silica. This law is long known to hold for the bcc solid helium-4. The characteristic temperatures of the threshold of the quasi-low temperature regime are found for the studied materials. The scaling in the specific heat of condensed matter is expressed by the dimensionless parameter, which is explored with the data for several glasses. The explanation of the correlation of the 'boson peak' temperature with the shear velocity is proposed. The critique of the Debye theory of specific heat and the Born-von Karman model of the lattice dynamics is given.