  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.
