If the zero-field transition in high temperature superconductors such as
YBa_2Cu_3O_7-\delta is a critical point in the universality class of the
3-dimensional XY model, then the general theory of critical phenomena predicts
the existence of a critical region in which thermodynamic functions have a
characteristic scaling form. We report the first attempt to calculate the
universal scaling function associated with the specific heat, for which
experimental data have become available in recent years. Scaling behaviour is
extracted from a renormalization-group analysis, and the 1/N expansion is
adopted as a means of approximation. The estimated scaling function is
qualitatively similar to that observed experimentally, and also to the
lowest-Landau-level scaling function used by some authors to provide an
alternative interpretation of the same data. Unfortunately, the 1/N expansion
is not sufficiently reliable at small values of N for a quantitative fit to be
feasible.Comment: 20 pages; 4 figure