One-dimensional classical adjoint SU(2) Coulomb Gas

TL;DR

This paper analyzes the equation of state of a one-dimensional classical SU(2) Coulomb gas, revealing confining and deconfining behaviors without a true phase transition, and discovering new collective phenomena at low densities and temperatures.

Contribution

It provides an exact solution for the equation of state of a 1D classical adjoint SU(2) Coulomb gas, highlighting its confinement properties and collective behavior.

Findings

Exhibits confinement at low densities and temperatures

Deconfinement occurs only at infinite densities and temperatures

Identifies a new collective behavior at low density and temperature

Abstract

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.