Differential Renormalization-Group Approach to the Layered sine-Gordon Model

TL;DR

This paper develops an exact renormalization group approach for the layered sine-Gordon model to better understand vortex behavior and the 3D/2D crossover in highly anisotropic high-temperature superconductors.

Contribution

It derives an exact RG equation for the layered sine-Gordon model using Wegner's approach, improving upon previous dilute gas approximations.

Findings

Derived an exact RG equation for the layered sine-Gordon model.

Found agreement between UV scaling laws and previous dilute gas results.

Proposed numerical solutions to enhance understanding of vortex dimensionality crossover.

Abstract

New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO 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 find by us by linearizing the RG equations with those obtained previously in the literature in the dilute gas approximation makes the improvement appearant which can be achieved by solving our RG equations numerically.