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

F. S. Nogueira

doi:doi:10.1209/epl/i1999-00211-3

DOI: 10.1209/epl/i1999-00211-3

Europhys. Lett, 45 (5), pp. 612-618 (1999)

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

F. S. Nogueira

Centre de Physique Théorique, Ecole Polytechnique - F-91128 Palaiseau Cedex, France

(received 23 September 1998; accepted in final form 4 January 1999)

PACS. 74.20De - Phenomenological theories (two-fluid, Ginzburg-Landau, etc.).
PACS. 11.10Hi - Renormalization group evolution of parameters.

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 established 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.

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