  We present a model to study effects from an external magnetic field, chemical
potential, and finite size, on the phase structure of a massive four- and
six-fermion interacting system. These effects are introduced by a method of
compactification of coordinates, a generalization of the standard Matsubara
prescription. Through the compactification of the $z$ coordinate and of
imaginary time, we describe a heated system with the shape of a film of
thickness $L$, at temperature $\beta^{-1}$ undergoing first- or second-order
phase transition. We have found a strong dependence of the temperature
transition on the constants couplings $\lambda$ and $\eta$. Besides magnetic
catalysis and symmetry breaking for both kinds of transition, we have found an
inverse symmetry breaking phenomenon with respect to first-order phase
transition.
