Anomalous dimensions and phase transitions in superconductors

Details Anomalous dimensions and phase transitions in superconductors Anomalous dimensions and phase transitions in superconductors

2000-05-24

arxiv.org/abs/cond-mat/0005418v3

Phys. Rev. B 62, 14559 (2000)

Physics

Condensed Matter

Superconductivity

RevTex, 20 pages, no figures; small changes; version accepted in PRB

Scientific paper

10.1103/PhysRevB.62.14559

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $\eta$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $\eta$ 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 $\eta_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $\sigma(\omega)\sim\xi^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.

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