Diamagnetic expansions for perfect quantum gases

In this work we study the diamagnetic properties of a perfect quantum gas in the presence of a constant magnetic field of intensity $B$. We investigate the Gibbs semigroup associated to the one particle operator at finite volume, and study its Taylor series with respect to the field parameter $\omega:= eB/c$ in different topologies. This allows us to prove the existence of the thermodynamic limit for the pressure and for all its derivatives with respect to $\omega$ (the so-called generalized susceptibilities).