Numerical simulations of Coulomb systems: A comparison between hyperspherical and periodic boundary conditions

Numerical simulations of Coulomb systems can be performed in various geometries, for instance in a cube with periodic boundary conditions (C-3) or on the surface of a hypersphere (S-3). We make a detailed comparison between electrostatics in these two geometries with a special emphasis on the problem of properly defining the zero of energy of a system of charges. This analysis enables the derivation of the correct configurational energies of important models of Coulombic fluids or plasmas in C-3 and S-3 in a unified way. The cases of the one component plasma and the restricted primitive model of electrolytes are considered in detail. (C) 1999 American Institute of Physics. [S0021- 9606(99)51234-8].