  The system we consider here is a charged fermions gas in the effective mass
approximation, and in grand-canonical conditions. We assume that the particles
are confined in a three dimensional cubic box $\Lambda$ with side $L\geq 1$,
and subjected to a constant magnetic field of intensity $ B \geq 0 $. Define
the grand canonical generalized susceptibilities $\chi_L^N$, $N\geq 1$, as
successive partial derivatives with respect to $B$ of the grand canonical
pressure $P_L$. Denote by $P_{\infty}$ the thermodynamic limit of $P_L$. Our
main result is that $\chi_L^N$ admit as thermodynamic limit the corresponding
partial derivatives with respect to $B$ of $P_{\infty}$. In this paper we only
give the main steps of the proofs, technical details will be given elsewhere.
