‘Screening’ of universal van der Waals–Casimir terms by Coulomb gases in a fully finitetwo-dimensional geometry

Abstract

This paper is a continuation of a previous one (Jancovici and Šamaj, 2004 J. Stat.Mech. P08006) dealing with classical Casimir phenomena in semi-infinite wallgeometries. In that paper, using microscopic Coulomb systems, the long-rangedCasimir force due to thermal fluctuations in conducting walls was shown to bescreened by the presence of an electrolyte between the walls into some residualshort-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 thegrand potentials for microscopic Coulomb systems confined in fully finite 2Dgeometries, in particular the disc geometry. Two cases are solved exactly: thehigh-temperature (Debye–Hückel) limit and the Thirring free-fermion point. Similarities andfundamental differences between fully finite and semi-finite geometries are pointed out.