One quantity considered in this model becomes zero at (*) van Hove singularities; that quantity is derived from the linear dispersion relation used in this model and is the density of states.
Applying this model to spin-waves in a ferromagnet gives a quantity proportional to the zeta function of 2.5, and only requires considering one polarization mode instead of three. This model can be modified with a quantity equal to the volume times the derivative of pressure with respect to energy at a given volume. The derivation of the energy in this model requires taking an integral whose limit is pi to the fourth over 15; that integral is the quantity x cubed over the quantity e to the power x minus 1, which gives its namesake's third number. In the original derivation of this model, an eighth of a sphere containing the one-third power of the quantity six over pi times N summands replaces a cube containing a similar number. One quantity considered in this model becomes zero at (*) van Hove singularities; that quantity is derived from the linear dispersion relation used in this model and is the density of states. At low temperatures, this model is sometimes modified by adding a linear contribution from electrons. This model recapitulates the Dulong-Petit law at high temperature, and considers the object in question as a collection of harmonic oscillators that oscillate together. In this model, the heat capacity takes on a temperature-cubed dependence, unlike the Einstein model. For 10 points, name this model of solids named for a Scottish physicist.
Applying this model to spin-waves in a ferromagnet gives a quantity proportional to the zeta function of 2.5, and only requires considering one polarization mode instead of three.
Debye model