Lebowitz-Penrose limit for continuum particle systems

We consider a particle system in $d\geq 2$ dimensions with an attractive Kac potential whose scaling parameter is $\gamma$ and a repulsive Kac potential with parameter $\gamma^{\frac{1}{2}}$. They have the same form as the corresponding potentials in \cite{LMP}, but in \cite{LMP} the scaling parameter was $\ga$ for both of them. We compute the \llp\ for the pressure and prove that the minimizers of the limit variational problem are spatially constant. The limit phase diagram has a liquid-vapour, of van der Waals type phase transition as, in \cite{LMP}