# Plasma living in a curved surface at some special temperature

## TL;DR

This paper presents exact solutions for a classical Coulomb plasma on curved surfaces at a specific temperature, highlighting the effects of surface curvature on plasma properties and densities.

## Contribution

It provides a unified analysis of exact solutions for Coulomb plasmas on curved geometries at a special temperature, emphasizing curvature's role.

## Key findings

- Exact analytic solutions exist at a special temperature for plasmas on curved surfaces.
- Surface curvature significantly influences plasma density and behavior.
- The solutions enhance understanding of Coulomb systems in curved geometries.

## Abstract

The simplest statistical mechanics model of a Coulomb plasma in two spatial dimensions admits an exact analytic solution at some special temperature in several (curved) surfaces. We present in a unifying perspective these solutions for the (non-quantum) plasma, made of point particles carrying an absolute charge $e$, in thermal equilibrium at a temperature $T=e^2/2k_B$, with $k_B$ Boltzmann's constant, discussing the importance of having an exact solution, the role of the curvature of the surface, and the densities of the plasma.