Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor

Abstract

If the zero-field transition in high-temperature superconductors such as YBa2Cu3O7−δ is a critical point in the universality class of the three-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 an attempt to calculate the universal scaling function associated with the specific heat, for which experimental data have become available in recent years. Scaling behavior 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.

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