Plasma living in a curved surface at some special temperature

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 $T=e^2\mathrm{/}2k_B$, 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.