Classical Coulomb fluids in a confined geometry

It has already been argued that a classical (three-dimensional) Coulomb fluid confined between two parallel walls exhibits ideal gas features when the distance between the walls becomes small; this is confirmed in the present paper. Two-dimensional models of Coulomb fluids (with a logarithmic interaction), confined in a strip, are also studied. These models do not become ideal gases in the narrow strip limit. The correlation functions are also studied. There is a special temperature at which exact results are obtained. At that temperature, the two-dimensional, two-component plasma (two-dimensional Coulomb gas), which is a conductor when unconfined, becomes a dielectric as soon as it is confined in a strip of noninfinite width. This can be understood as a displacement of the Kosterlitz-Thouless transition by the confinement.