Coulomb systems seen as critical systems: Ideal conductor boundaries

Abstract

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 ad-dimensional (d≥2) Coulomb system confined in a slab of thicknessW, the grand potential (in units ofk _B T) per unit area has the universal term Γ(d/2)ζ(d)/2^dπ^d/2W^d−1. For a two-dimensional Coulomb system confined, in a disk of radiusR, the grand potential (in units ofk _B T) has the universal term (1/6) lnR. These results, of general validity, are checked on two-dimensional solvable models.