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Anomalous dimensions and phase transitions in superconductors

Flavio S. Nogueira
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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 $η_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $σ(ω)\simξ^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.

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Flavio S. Nogueira. 2000-09-07. Anomalous dimensions and phase transitions in superconductors. https://doi.org/10.1103/physrevb.62.14559

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