On lattices with finite Coulombian interaction energy in the plane

Abstract

Given a discrete set $Λ$ 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 $Λ$ with a uniform negative background of density $m\in\R$. It is defined in several steps, following mostly \cite{ss1}.