A Review of the Real Space Renormalization Group Analysis of the Two- Dimensional Coulomb Gas, the Kosterlitz-Thouless-Berezinski Transition, and Extensions to a Layered Vortex Gas

TL;DR

This paper reviews the real-space renormalization group analysis of the Kosterlitz-Thouless transition in 2D systems, discusses its signatures in experiments, and extends the analysis to layered superconductors, exploring critical phenomena and crossover behaviors.

Contribution

It provides a comprehensive review of the RG analysis of the KTB transition and extends the methodology to layered vortex systems, including effects of finite currents and 3D crossover.

Findings

Derivation of the temperature dependence of correlation length.

Signatures of the KTB transition in electronic transport.

Analysis of 3D critical region and crossover effects.

Abstract

Fundamental properties of the Kosterlitz-Thouless-Berezinskii (KTB) transition which occurs in systems in the universality class of the two-dimensional X-Y model are reviewed here with an emphasis on the real-space renormalization group analysis used to derive the recursion relations. A derivation of the unique temperature dependence of the correlation length of this system will be presented and the signatures of the KTB transition in electronic transport measurements will be explained. Extensions of this model and technique to layered superconductors will also be presented. The size of the 3D critical region, the nature of the 3D crossover, and the effect of a finite electric current will be discussed.