  It is considered in this work the phase transition patterns for a coupled
two-scalar field system model under the combined effects of finite sizes and
temperature. The scalar fields are taken as propagating in a D=4 Euclidean
space with the usual periodic compactification in the Euclidean time direction
(with dimension given by the inverse of the temperature) and also under a
compact dimension in the space direction, which is restricted to size L. In the
latter case, a Dirichlet boundary condition is considered. Finite-size
variation of the critical temperature for the cases of symmetry restoration and
inverse symmetry breaking are studied. At fixed finite-temperature values, the
variation of the inverse correlation lengths with the size L might display a
behavior analogous to reentrant phase transitions. Possible applications of our
results to physical systems of interest are also discussed.
