Violation of finite-size scaling for the free energy near criticality

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The singular part of the finite-size free energy density fₛ of the O(n) symmetric ϕ⁴ 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 fₛ near Tc. 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 Tc for both periodic and Dirichlet boundary conditions.