Journal of Statistical Physics. Vol. 84, Nos. 3/4, 1996, p. 359-378.
Coulomb systems in which the particles interact through the d-dimensional
Coulomb potential but are confined in a fiat manifold of dimension d-1 are
considered. The actual Coulomb potential acting is defined by particular bound-
ary conditions involving a characteristic macroscopic distance W in the direc-
tion perpendicular to the manifold: either it is periodic of period W in that
direction, or it vanishes on one ideal conductor wall parallel to the manifold at
a distance W from it, or it vanishes on two parallel walls at a distance W from
each other with the manifold equidistant from them. Under the assumptions
that classical equilibrium statistical mechanics is applicable and that the system
has the macroscopic properties of a conductor, it is shown that the suitably
smoothed charge correlation function is universal, and that the free energy and
the grand potential have universal dependences on W (universal means inde-
pendent of the microscopic detail). The cases d=2 are discussed in detail, and
the generic results are checked on an exactly solvable model. The case d= 3 of
a plane parallel to an ideal conductor is also explicitly worked out.