  Given a discrete set $\Lambda$ in the plane (we will also say a {\em
lattice}) and a real number $m\ge 0$, the renormalized energy introduced in
\cite{ss1} heuristically describes the interaction energy of unit charges
placed at the points of $\Lambda$ with a uniform negative background of density
$m\in\R$. It is defined in several steps, following mostly \cite{ss1}.
