On the Magnetization of a Charged Bose Gas in the Canonical Ensemble

Abstract

Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side $L\geq 1$ and subjected to a constant magnetic field $B\neq 0$. If the bulk density of particles $\rho$ and the temperature $T$ are fixed, then define the canonical magnetization as the partial derivative with respect to $B$ of the reduced free energy. Our main result is that it admits thermodynamic limit for all strictly positive $\rho$, $T$ and $B$. It is also proven that the canonical and grand canonical magnetizations (the last one at fixed average density) are equal up to the surface order corrections.