Coulomb systems seen as critical systems: Ideal conductor boundaries

When a classical Coulomb system has macroscopic conducting behavior, its grand potential has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system: the massless Gaussian field. Here, the Coulomb system is assumed to be confined by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For a a-dimensional (d greater than or equal to 2) Coulomb system confined in a slab of thickness W, the grand potential (in units of k(B)T) per unit area has the universal term Gamma(d/2) zeta(d)/2(d) pi(d/2)W(d-1). For a two-dimensional Coulomb system confined in a disk of radius R, the grand potential (in units of k(B)T) has the universal term (1/6) In R. These results, of general validity, are checked on two-dimensional solvable models.