Finite-size, magnetic and chemical-potential effects on first-order phase transitions

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.