Differential renormalization-group approach to the layered sine-Gordon model

Abstract

A new qualitative view of vortex length–scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic Bi₂Sr₂CaCu₂O₈ single crystals in zero magnetic field. This indicates the need for a better description of the 3D/2D crossover in vortex dimensionality. The vortex-dominated properties of high transition temperature superconductors with extremely high anisotropy (layered systems) are reasonably well described in the framework of the layered XY model which can be mapped onto the layered sine-Gordon model. For the latter we derive an exact renormalization group (RG) equation using Wegner's and Houghton's approach in the local potential approximation. The agreement of the UV scaling laws found by us by linearizing the RG equations with those obtained previously in the literature in the dilute gas approximation makes apparent the improvement which can be achieved by solving our RG equations numerically.

Acknowledgements

I.N. takes great pleasure in acknowledging discussion with K. Vad, S. Mészáros and U.D. Jentschura. This work has been supported by the grant OTKA T032501/00 and also partially by the grant OTKA M041537 and the Supercomputing Laboratory of the Faculty of Natural Sciences, University of Debrecen. Nándori would like to thank the Max-Planck Institute for Nuclear Physics, Heidelberg, for the kind hospitality extended on the occasion of being a guest researcher in 2004 during which part of this work was completed.