Anomalous dimensions and phase transitions in superconductors
Flavio S. Nogueira
DOI 10.1103/PhysRevB.62.14559 · Physical Review B
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Abstract
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 implies the existence of a Lifshitz point 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.
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