Anomalous dimensions and phase transitions in superconductors

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the η exponent is a consequence of a special singular behavior in momentum space. The negative sign of η comes from the divergence of the critical correlation function at finite distances. This behavior is related to the existence of a firstorder transition in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential ηA = 4 − d has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling σ(ω) ∼ ξz−2. The prediction z ≈ 3.7 is obtained from existing Monte Carlo data. A different prediction is made on the basis of duality arguments, giving z = 5/2. We discuss about the discrepancy between these predictions. Pacs: 74.20.-z, 05.10Cc, 11.25.Hf Typeset using REVTEX 1