The Debye model replaces the crystal's vibrational spectrum by a continuum of phonon modes up to a cutoff chosen to preserve the total number of vibrational degrees of freedom.
The Debye model is a theoretical framework used to describe the specific heat capacity of solids, particularly at low temperatures. Developed by physicist Peter Debye in 1912, it extends the classical Einstein model of specific heat by considering acoustic phonons, or quantized lattice vibrations, in a more comprehensive manner.
Wikipedia mentions that it is completely analogous to Planck's law.
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