Positive and negative charged rods alternating along a line: Exact results

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a line with the charges alternating in sign along the line is considered. By replacing the line with a lattice, one can calculate the grand partition function and correlations exactly for one value of the coupling constant. The exact solution exhibits features forbidden in the corresponding continuous system, in which each pair of oppositely charged rods also interact via a short-range repulsive potential, and there is no restriction on the ordering of the charges. The sum rule indicating the phase of the system is identified.