Journal of Statistical Physics, Vol. 94, Nos. 56, 1999. p. 955-1025.
We consider particles in R^d , d>/2, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean-field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquidgas phase transition when the interaction range is finite but long compared to the interparticle spacing for a range of temperature.