  The order parameter of a critical system defined in a layered parallel plate
geometry subject to Neumann boundary conditions at the limiting surfaces is
studied. We utilize a one-particle irreducible vertex parts framework in order
to study the critical behavior of such a system. The renormalized vertex parts
are defined at zero external quasi-momenta, which makes the analysis
particularly simple. The distance between the boundary plates $L$
characterizing the finite size system direction perpendicular to the
hyperplanes plays a similar role here in comparison with our recent unified
treatment for Neumann and Dirichlet boundary conditions. Critical exponents are
computed using diagrammatic expansion at least up to two-loop order and are
shown to be identical to those from the bulk theory (limit $L \rightarrow
\infty$).
