de Haas-van Alphen Effect and the Specific Heat of an Electron Gas

A model electron gas is studied in order to provide a microscopic justification of the Shoenberg conjecture that the harmonic content of the de Haas-van Alpen oscillations of the magnetization →M can properly be explained by replacing the applied field →H in the elementary expression for →M(→H) by the total induction →B=→H+→M. The model contains a current-current interaction between the electrons; and it is shown that the unscreened long-range nature of this interaction leads to a term in the low-temperature specific heat proportional to T lnT. For a gas with terrestrial densities the coefficient of this anomalous term is very small and probably beyond detection.