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

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.