Solvable isotherms for a two-component system of charged rods on a line

Abstract

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constantΓ=q 2/k B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity planeξ, all the zeros of the grand partition function lie on the negative real axis forΓ 2. In addition, forΓ>4, we conjecture in general and prove atΓ=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.