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.

In this work we analyze the finite-volume and magnetic effects on the phase structure of a generalized version of Nambu-Jona-Lasinio model with three quark flavors. By making use of mean-field approximation and Schwinger's proper-time method in a toroidal topology with antiperiodic conditions, we investigate the gap equation solutions under the change of the size of compactified coordinates, strength of magnetic field, temperature and chemical potential. The 't Hooft interaction contributions are also evaluated. The thermodynamic behavior is strongly affected by the combined effects of relevant variables. The findings suggest that the broken phase is disfavored due to both increasing of temperature and chemical potential, and the drop of the cubic volume of size L, whereas it is stimulated with the augmentation of magnetic field. In particular, the reduction of L (remarkably at L ≈ 0.5 − 3 fm) engenders a reduction of the constituent masses for u, d, s-quarks through a crossover phase transition to the their corresponding current quark masses. On the other hand, the presence of a magnetic background generates greater values constituent quark masses, inducing smaller sizes and greater temperatures at which the constituent quark masses drop to the respective current ones.

We study effects coming from finite size, chemical potential and from a magnetic background on a massive version of a four-fermion interacting model. This is performed in four dimensions as an application of recent developments for dealing with field theories defined on toroidal spaces. We study effects of the magnetic field and chemical potential on the size-dependent phase structure of the model, in particular, how the applied magnetic field affects the size-dependent critical temperature. A connection with some aspects of the hadronic phase transition is established.