The 2-d Coulomb Gas on a 1-d lattice

TL;DR

This paper investigates a 2D Coulomb gas constrained to a 1D ring, providing exact results on phase transitions, correlations, and phase characterization, supported by simulations and connecting to broader physical problems.

Contribution

It establishes exact self-duality and transition temperature for the sine-Gordon model in this setting, offering asymptotic correlation results and phase analysis.

Findings

Exact self-duality and transition temperature identified.

Asymptotically exact correlation functions derived.

Numerical simulations support theoretical predictions.

Abstract

The statistical mechanics of a two dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low and high temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, the quantum Brownian motion of a particle in a periodic potential and impurity problems, are pointed out.