Perfect Screening for Charged Systems

It is proven that when correlations in an equilibrium classical system in $\nu$ dimensions, $\nu >~2$, containing charges decay faster than ${\left(\mathrm{distance}\right)}^{-(l+\nu )}$ then the charge cloud surrounding particles has no multipole moments of order $k<~l$. This yields $l+1\mathrm{}$ sum rules with $l=\infty$ when the decay is exponential. This extends previous results for $l<~2$ sum rules and also generalizes them to systems containing fixed dipoles (or higher multipoles). Some consequences are described.