Gauge dependence of the order parameter anomalous dimension in the Ginzburg-Landau model and the critical fluctuations in superconductors

The critical fluctuations of superconductors are discussed in a fixed dimension scaling suited to describe the type-II regime. The gauge dependence of the anomalous dimension of the scalar field is established exactly from the Ward-Takahashi identities. Its fixed-point value gives the η critical exponent and it is shown that η is gauge independent, as expected on physical grounds. In the scaling considered, η is found to be zero at 1-loop order, while ν ∼ 0.63. This result is just the 1-loop values for the XY model obtained in the fixed-dimension renormalization group approach. It is shown that this XY behavior holds at all orders. The result η = ηXY should be contrasted with the negative values frequently reported in the literature. (orig.)