Journal of Statistical Physics, Vol. 120, Nos. 1/2, July 2005. p. 125-146.
DOI: 10.1007/s10955-005-5477-8
We study physical situations when one or two "guest" arbitrarily-charged particles are immersed in the bulk of a classical electrolyte modelled by a Coulomb gas of ± unit point-like charges, the whole system being in thermal equilibrium. The models are treated as two-dimensional with logarithmic pairwise interactions among charged constituents; the (dimensionless) inverse temperature beta is considered to be smaller than 2 in order to ensure the stability of the electrolyte against the collapse of positive-negative pairs of charges. Based on recent progress in the integrable (l + l)-dimensional sine-Gordon theory, exact formulas are derived for the chemical potential of one guest charge and for the asymptotic large-distance behavior of the effective interaction between two guest charges. The exact results imply, under certain circumstances, anomalous effects such as an effective attraction (repulsion) between like-charged (oppositely-charged) guest particles and the charge inversion in the electrolyte vicinity of a highly-charged guest particle. The adequacy of the concept of renormal-ized charge is confirmed in the whole stability region of inverse temperatures and the related saturation phenomenon is revised.