Study of two-dimensional electrons in a magnetic field. II. Intermediate field

Taking into consideration the first-order-exchange and ring diagrams, we present a theory of two-dimensional (2-D) electrons in a magnetic field under the de Haas-van Alphen condition. The Fermi momentum or the chemical potential of the system oscillates with the magnetic field, its interaction term being characterized by a factor (e²p₀)3/4=(21/2rₛ)3/4. Due to a 2-D peculiarity, the susceptibility oscillates as in the ideal case without a constant phase -π4 characteristic of the three-dimensional case. A relation between the amplitude of the oscillating susceptibility and the field and temperature is derived. The energy variation is like a⁴cos(πε₀a²), where a² represents the field energy and ε₀ is the Fermi energy for the ideal case, i.e., 2π, in the units =1 and $2m=1$, where n is the number density. The amplitude of the energy oscillation increases with the field strength squared. A new specific-heat formula is also presented.