  Finite temperature quantum field theory in the heat kernel method is used to
study the heat capacity of condensed matter. The lattice heat is treated a la
P. Debye as energy of the elastic (sound) waves. The dimensionless functional
of free energy is re-derived with a cut-off parameter and used to obtain the
specific heat of crystal lattices. The new dimensionless thermodynamical
variable is formed as the Planck's inverse temperature divided by the lattice
constant. The dimensionless constant, universal for a class of crystal
lattices, which determines the low temperature region of molar specific heat,
is introduced and tested with the data for diamond lattice crystals. The low
temperature asymptotics of specific heat is found to be the fourth power in
temperature instead of the cubic power law of the Debye theory. Experimental
data for the carbon group elements (silicon, germanium) and other materials
decisively confirm the quartic law. The true low temperature regime of specific
heat is defined by the surface heat, therefore, it depends on geometrical
characteristics of a body, while the absolute zero temperature limit is
geometrically forbidden. The limit on a growth of specific heat at temperatures
close to critical points, known as the Dulong-Petit law, appears from the
lattice constant cut-off. Its value depends on the lattice type and it is the
same for materials with the same crystal lattice. The Dulong-Petit values of
compounds are equal to those of elements with the same crystal lattice type, if
one mole of solid state matter were taken as the Avogadro number of the lattice
atoms. This means the Neumann-Kopp rule is valid only in some cases.
