In classical equilibrium statistical mechanics, the two-dimensional two-component Coulomb gas is exactly solvable at the special value of the reduced inverse temperature r = 2. This is used for building an exactly solvable model of the electrical double layer. A charged hard wall (primitive electrode), a polarizable interface, an ideal conductor electrode, a semipermeable membrane are studied: the density profiles and correlation functions are computed. The differential capacity and the surface tension are also obtained.
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