Nonuniversal size dependence of the free energy of confined systems near criticality

The singular part of the finite-size free-energy density f(s) of the O(n) symmetric Phi(4) field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-n limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a leading nonuniversal L dependence of f(s) near T-c. This implies a significant restriction for the validity of universal finite-size scaling for model systems and real systems. For film geometry we predict a leading nonuniversal contribution to the critical Casimir force above the superfluid transition of He-4.