A Testbench for the Nested Dipole Hypothesis of Kosterlitz and Thouless

TL;DR

This paper tests the nested dipole hypothesis in the Kosterlitz-Thouless transition of a 2D plasma model by comparing theoretical predictions with exact solutions, confirming the hypothesis's validity.

Contribution

It provides an explicit verification of the nested dipole hypothesis using an exactly solvable 2D plasma model near a metal wall.

Findings

Agreement between theoretical predictions and exact solutions.

Validation of the nested dipole hypothesis.

Insights into the Kosterlitz-Thouless transition mechanisms.

Abstract

We consider the two-dimensional one-component plasma without a background and confined to a half plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse power law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analysing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular we calculate the asymptotic density profile by resumming its low fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.