  In this work we investigate the finite-size effects on the phase structure of
a two-flavor four-fermion interaction model with a flavor-mixing four-body
interaction and in the presence of a magnetic background, taking into account
different boundary conditions. We employ mean-field approximation and
Schwinger's proper-time method in a toroidal topology with antiperiodic and
periodic boundary conditions. The chiral susceptibility and constituent quark
masses are studied under the change of the relevant parameters: size of
compactified coordinates, temperature, chemical potential and magnetic field
strength, within the different scenarios of boundary conditions and the value
of flavor-mixing parameter. The findings suggest that the thermodynamic
behavior of this system is strongly affected by the combined effects of
relevant variables, depending on the range of their change, the value of
flavor-mixing parameter and the choice of boundary conditions.
