Statistical mechanics of nonrelativistic charged particles in a constant magnetic field

The statistical mechanics of a system of nonrelativistic charged particles in a constant magnetic field is discussed. The spatial dimension D is arbitrary, with D>or=3 assumed. Calculations are presented from first principles using the effective action method. For D>or=5 the system has a phase transition with a Bose condensate. We show how the effective action method deals in a very natural way with the condensate, and study its role in the magnetization of the gas. For large values of the magnetic field we show how the magnetized gas in D spatial dimensions behaves like the free Bose gas in D-2 spatial dimensions. Even though for D=3 the magnetized gas does not have a phase transition for any nonzero value of the magnetic field, we show how the specific heat starts to resemble the result for the free gas as the magnetic field is reduced. A number of analytical approximations for the magnetization and specific heat are given, and compared with numerical results. In this way we are able to study in precise detail how the B-->0 limit of the magnetized gas is achieved.