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

Abstract

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.

Keywords:

• Lekner summations
• Ewald summations
• Quasi-two-dimensional systems

Acknowledgements

I acknowledge the computation facilities of the Centre de Ressources Informatiques (CRI) de l'Université de Paris-Sud. All the computations performed in this work were carried out on a Silicon Graphics Origin 2000 (R10000/195 processors). I am very grateful to Professor J. Lekner for having sent his work to me on the Energetics of hydrogen ordering in ice (Physica B, 252, 149 (1998)) and to Dr. V. Huet for her help in the preparation of the manuscript.

Notes

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Additional information

Notes on contributors

Martial Mazars *

e-mail: [email protected]