Universality in some classical Coulomb systems of restricted dimension

Abstract

Coulomb systems in which the particles interact through the $d$-dimensional Coulomb potential but are confined in a flat manifold of dimension $d-1$ are considered. The Coulomb potential is defined with some boundary condition involving a characteristic macroscopic distance $W$ in the direction 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 independent 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.

24 pages,TEX

References in corpus (2)

• Classical Coulomb Systems:Screening and Correlations Revisited
• Coulomb Systems Seen as Critical Systems: Ideal Conductor Boundaries

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