Equation of state in the fugacity format for the two-dimensional Coulomb gas

TL;DR

This paper derives an exact equation of state in the fugacity format for the 2D Coulomb gas in the conducting phase, providing explicit expansions and validating results with Monte Carlo simulations.

Contribution

It presents the first exact form of the equation of state in fugacity format for the 2D Coulomb gas above the Kosterlitz-Thouless transition, including explicit short-distance expansions.

Findings

Good agreement with Monte Carlo simulations at low density

Explicit expansion up to order ζ^6 in activity

Valid for temperatures above the Kosterlitz-Thouless transition

Abstract

We derive the exact general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz-Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order $O(\zeta^6)$ in the activity $\zeta$. Our results are in very good agreement with Monte Carlo simulations at very low density.