  In the following paper, we will study a charged scalar field under an
electromagnetic external field taking into account the spatial confining of the
system. We shall use the Coleman-Weinberg method in one-loop approximation to
obtain the effective potential of the model in the proper time representation.
Through generalized Matsubara formalism, we applied several kinds of boundary
conditions on the frontier of the system. The regularization of the model is
performed by a scheme independent of the external electromagnetic applied
field. The model presents phase transition and we carry out its analysis by the
free energy density functional of the bosonic system. The findings show
magnetic catalysis, electric catalysis, and inverse electric catalysis
phenomena, all of them depending on the thickness of the system.
