Wigner solids, classical Coulomb lattices, and invariant average potential

Abstract

We show that Hall's analysis of $K$ for Wigner solids, the Ihm and Cohen analysis of the Fuchs energy $\epsilon$, some extensions of Hall's analysis, and some recent results for the classical Coulomb-lattice model provide a tight theoretical framework useful beyond the matter of Hall's conclusions about the $\epsilon$ for Wigner solids based on an incorrect relation accepted from the literature. We also comment on spherical approximations.