Lekner summations and Ewald summations for quasi-two-dimensional systems

The purpose of this work is to carry out a comparison between the Ewald quasi-2D and Lekner summation methods. These methods were derived to treat the long-range electrostatic interactions in systems periodic in two directions, but bound in the third. The comparison is performed by Monte Carlo simulations on a very simple system, a bilayer of point ions; samplings of the phase space, average energies and structure functions are compared. When correctly implemented, the Lekner summation method is found to be in close agreement with the Ewald quasi-2D method; otherwise, a very complicated bias may plague computations.