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We present a model to study effects from an external magnetic field, chemicalpotential, and finite size, on the phase structure of a massive four- andsix-fermion interacting system. These effects are introduced by a method ofcompactification of coordinates, a generalization of the standard Matsubaraprescription. Through the compactification of the $z$ coordinate and ofimaginary time, we describe a heated system with the shape of a film ofthickness $L$, at temperature $\beta^{-1}$ undergoing first- or second-orderphase transition. We have found a strong dependence of the temperaturetransition on the constants couplings $\lambda$ and $\eta$. Besides magneticcatalysis and symmetry breaking for both kinds of transition, we have found aninverse symmetry breaking phenomenon with respect to first-order phasetransition.

A Model to Study Finite-Size and Magnetic Effects on the Phase Transition of a Fermion Interacting System