2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112571Consider 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 $ρ$ 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 $ρ$, $T$ 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.Appeared in Communications in Mathematical PhysicsMathematical Physics82B10; 81Q10text