1 7 M ay 2 00 5 “ Screening ” of universal van der Waals – Casimir terms by Coulomb gases in a fully - finite two - dimensional geometry

" Screening " of universal van der Waals – Casimir terms by Coulomb gases in a fully-finite two-dimensional geometry Abstract. This paper is a continuation of a previous one [Jancovici B andŠamaj L, 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-Hückel) limit and the Thirring free-fermion point. Similarities and fundamental differences between fully-finite and semi-finite geometries are pointed out.