  We discuss, from a geometric standpoint, the specific heat of a solid. This
is a classical subject in solid state physics which dates back to a pioneering
work by Einstein (1907) and its refinement by Debye (1912). Using a special
quantization of crystal lattices and calculating the asymptotic of the
integrated density of states at the bottom of the spectrum, we obtain a
rigorous derivation of the classical Debye $T^3$ law on the specific heat at
low temperatures. The idea and method are taken from discrete geometric
analysis which has been recently developed for the spectral geometry of crystal
lattices.
