Correlations in two-component log-gas systems

TL;DR

This paper investigates the particle and charge correlation functions in a two-dimensional Coulomb gas confined to a line, revealing a Kosterlitz-Thouless transition at a critical coupling and analyzing correlation decay behaviors.

Contribution

It provides a systematic analysis of correlation functions in two-component log-gas systems, including perturbation and low-fugacity expansions, and derives renormalization equations.

Findings

Identifies a zero-density Kosterlitz-Thouless transition at b3=2.

Establishes an O(1/r^4) decay of correlations in the high-temperature limit.

Resums low-fugacity expansion to all orders, deriving renormalization equations.

Abstract

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless type transition as the dimensionless coupling $\Gamma := q^2 / kT$ is varied through $\Gamma = 2$. In the charge ordered system we use a perturbation technique to establish an $O(1/r^4)$ decay of the two-body correlations in the high temperature limit. For $\Gamma \rightarrow 2^+$, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations.