Lower bounds for thermodynamic quantities of two- and three-dimensional one-component plasmas

Exact lower bounds for the correlation energy of the one-component plasmas (OCP) with the $r^{-1\mathrm{}}$ potential are given in $d$ dimensions $1<d\le 3$. For classical OCP's with $d=2\mathrm{} \mathrm{and} 3$, this lower bound contains most of the correlation energy in the high-density domain, and the residue is given by two integrals of positive-definite functions, including the pair correlation function and the structure factor. For the classical OCP with $d=3\mathrm{}$, a lower bound which improves upon known ones due to Mermin and to Lieb and Narnhofer in the domain $\Gamma <15.3\mathrm{}$ is given.