"Screening" of universal van der Waals - Casimir terms by Coulomb gases in a fully-finite two-dimensional geometry

TL;DR

This paper investigates how universal Casimir terms in finite 2D Coulomb systems are screened by electrolyte effects, extending previous semi-infinite wall studies to fully finite geometries like discs, with exact solutions at specific limits.

Contribution

It extends the understanding of Casimir force screening to fully finite 2D geometries, providing exact results at high temperature and free-fermion points.

Findings

Universal Casimir terms are screened in finite geometries.

Exact solutions obtained at high-temperature and free-fermion limits.

Differences between finite and semi-infinite geometries are highlighted.

Abstract

This paper is a continuation of a previous one [Jancovici and Samaj, 2004 J. Stat. Mech. P08006] dealing with classical Casimir phenomena in semi-infinite wall geometries. In that paper, using microscopic Coulomb systems, the long-ranged Casimir force due to thermal fluctuations in conducting walls was shown to be screened by the presence of an electrolyte between the walls into some residual short-ranged force. Here, we aim to extend the study of the screening (cancellation) phenomena to universal Casimir terms appearing in the large-size expansions of the grand potentials for microscopic Coulomb systems confined in fully-finite 2D geometries, in particular the disc geometry. Two cases are solved exactly: the high-temperature (Debye-H\"uckel) limit and the Thirring free-fermion point. Similarities and fundamental differences between fully-finite and semi-infinite geometries are pointed out.