Abstract
We obtain explicit expressions for thermodynamic quantities of a relativistic degenerate free electron gas in a magnetic field in terms of Hurwitz zeta functions. The formulation allows for systematic expansion in all regimes. Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy E F, the temperature T and an energy related to the magnetic field or Landau level spacing, eB/ E F. We study the cold and warm scenarios, T⪡ eB/ E F and eB/ E F⪡ T, respectively. We reproduce the oscillations of the magnetization as a function of the field in the cold regime and the dilution of them in the warm regime.
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