  We study temperature and finite-size effects on the spontaneous symmetry
breaking/restoration for a scalar field model under the influence of an
external magnetic field, at finite chemical potential. We use the 2PI formalism
and consider the large-$N$ limit. We find that there is a minimal size of the
system to sustain the broken phase, which diminishes as the applied field
increases but is independent of the chemical potential. We analyze the critical
curves and show that the magnetic field enhances the broken-phase regions,
while increasing the chemical potential leads to a diminishement of the
critical temperature.
