Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field

Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular magnetic field are derived. This is accomplished by first deriving the general expression for the thermodynamical potential, and then employing this result to obtain the corresponding expression for the two-dimensional gas. The chemical potential and magnetization are studied as a function of temperature and magnetic field, and shown to be in agreement with prior work. It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.