Neumann boundary conditions with null external quasi-momenta in finite-systems

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 $L \rightarrow \infty$).