Interaction between two rows of localized adsorption sites in a 2D one-component plasma

We compute the free energy for two rows of localized adsorption sites embedded in a two dimensional one-component plasma with neutralizing background density ρ. The interaction energy between the adsorption sites is repulsive. We also compute the average occupation number of the adsorption sites and compare it to the result for a single row of sites. The exact result indicates that the discretization does not induce charge asymmetry and no attractive forces occur.