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 
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