Editing Debye model (section)

== Extension to other quasi-particles ==
For other [[boson]]ic [[quasi-particle]]s, e.g., [[magnon]]s (quantized spin waves) in ferromagnets instead of the [[phonons]] (quantized sound waves), one can derive analogous results. In this case at low frequencies one has different dispersion relations of momentum and energy, e.g., <math>E(\nu )\propto k^2</math> in the case of magnons, instead of <math>E(\nu )\propto k</math> for phonons (with <math>k=2\pi /\lambda </math>). One also has different density of states (e.g., <math>\int g(\nu ){\rm d}\nu \equiv N\,</math>). As a consequence, in ferromagnets one gets a magnon contribution to the heat capacity, <math>\Delta C_{\,{\rm V|\,magnon}}\,\propto T^{3/2}</math>, which dominates at sufficiently low temperatures the phonon contribution, <math>\,\Delta C_{\,{\rm V|\,phonon}}\propto T^3</math>. In metals, in contrast, the main low-temperature contribution to the heat capacity, <math>\propto T</math>, comes from the electrons. It is [[Fermion gas|fermion]]ic, and is calculated by different methods going back to [[Arnold Sommerfeld|Sommerfeld]]'s [[free electron model]].{{Citation needed|date=January 2024}}