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 arbit rary, with D greater than or equal to 3 assumed. Calculations are presented from first principles using the effective action method. For D greater tha n or equal to 5 the system has a phase transition with a Bose condensate. W e 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 di mensions behaves like the free Bose gas in D-2 spatial dimensions. Even tho ugh for D=3 the magnetized gas does not have a phase transition for any non zero value of the magnetic field, we show how the specific heat Starts to r esemble the result for the free gas as the magnetic field is reduced. A num ber of analytical approximations for the magnetization and specific heat ar e given, and compared with numerical results. In this way we are able to st udy in precise detail how the B-->0 limit of the magnetized gas is achieved . [S1063-651X(99)08211-2].