Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas

TL;DR

This paper rigorously analyzes the behavior of the two-dimensional Coulomb Gas along the Kosterlitz-Thouless transition line using a renormalization group approach, focusing on the pressure near the phase boundary.

Contribution

It provides a rigorous mathematical study of the Coulomb Gas pressure along the Kosterlitz-Thouless transition line using renormalization group techniques.

Findings

Characterization of the pressure behavior near the transition line

Rigorous proof of properties of the Coulomb Gas at the phase boundary

Insights into the dipole region boundary in phase space

Abstract

With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the boundary of the dipole region in the activity-temperature phase-space.