Screening-approximation prediction of peaking in the specific heat of a superconducting film

All contributions to the free energy of $O(n)$ and of $O(1)$ are computed for an $n$-component two-dimensional Ginzburg-Landau field. The $O(1)$ terms correspond to ring diagrams, and their sum constitutes the first-order screening approximation. The second derivative of the free energy with respect to temperature yields a predicted specific heat for $n=2$ which peaks, in qualitative disagreement with the monotonic temperature variation found experimentally for a superconducting film by Zally and Mochel.