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

TL;DR

This paper investigates the gauge dependence of the anomalous dimension in the Ginzburg-Landau model, demonstrating that the critical exponent η is gauge independent and matches XY model predictions, with implications for understanding superconducting fluctuations.

Contribution

It establishes the gauge independence of the anomalous dimension η and shows that its value aligns with the XY model at all orders, clarifying discrepancies in previous literature.

Findings

η is gauge independent and equals the XY model value

At 1-loop order, η=0 and ν≈0.63

The XY behavior of η holds at all orders

Abstract

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 stablished exactly from the Ward-Takahashi identities. Its fixed point value gives the $\eta$ critical exponent and it is shown that $\eta$ is gauge independent, as expected on physical grounds. In the scaling considered, $\eta$ is found to be zero at 1-loop order, while $\nu\approx 0.63$. 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 $\eta=\eta_{XY}$ should be contrasted with the negative values frequently reported in the literature.