  We perform a study about effects of an applied magnetic field and a finite
chemical potential on the size-dependent phase structure of a first-order
transition. These effects are introduced by using methods of quantum fields
defined on toroidal spaces, and we study in particular the case of two
compactified dimensions, imaginary time and a spatial one (a heated film). It
is found that for any value of the applied field, there is a minimal size of
the system, independent of the chemical potential, below which the transition
disappears.
