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The simplest statistical mechanics model of a Coulomb plasma in two spatialdimensions admits an exact analytic solution at some special temperature inseveral (curved) surfaces. We present in a unifying perspective these solutionsfor the (non-quantum) plasma, made of point particles carrying an absolutecharge $e$, 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.

Plasma living in a curved surface at some special temperature