  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 non-universal L
dependence of $f_s$ near $T_c$. For film geometry this implies a non-universal
critical Casimir force with an algebraic L dependence that dominates the
exponential finite-size scaling behavior above $T_c$ for both periodic and
Dirichlet boundary conditions.
