Comments on the electrostatic energy of a Wigner solid

Abstract

A recent contention by Hall that Fuchs's calculation of the electrostatic energy of an infinite Wigner solid contains a fundamental error is not true. Fuchs calculated the average electrostatic energy per electron ${\ensuremath{\Phi}}_{i}$, while Hall derived this quantity from the energy of the interaction of one electron with the rest of the lattice ${\ensuremath{\Phi}}_{\mathrm{el}}$ by use of the relation ${\ensuremath{\Phi}}_{i}=(\frac{1}{2}){\ensuremath{\Phi}}_{\mathrm{el}}$; however, this relation is not valid in the case studied by Hall. Preliminary results for finite Wigner solids are discussed.