The statistical mechanics of an electron gas in a uniform magnetic field is developed based on a diagram technique. To zero-order exchange graphs, the pair-distribution function is evaluated with electronic spins taken into consideration. The result can be used to obtain the susceptibility to first order in interaction for both high and low temperatures. Under the de Haas-van Alphen (dHvA) condition, the exchange graphs yield not only a nonoscillating susceptibility but also oscillating waves with the same basic frequency as the free-particle waves. These exchange waves, however, have different analytical expressions with different magnetic field dependence from those of free-particle waves. Indeed, higher harmonics play more important roles than the case of free-particle waves. Therefore, the superposed waves can change shape significantly with small change of parameters such as the Fermi energy. The exchange graphs add fine rippling waves to the main dHvA waves due to free electrons. Also the graphs give an account of the Shoenberg-Dingle plot for the magnetic field dependence of the amplitude of dHvA waves. However, the plot may not be a straight line. Explicit numerical evaluations of dHvA waves are performed by using CDC 6400. The ring diagrams are found to yield a contribution similar to the exchange graphs.

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