Liquid-Vapor Phase Transitions for Systems with Finite Range Interactions

We consider particles in $\R^d, d \geq 2$ 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 liquid-gas phase transition, when the interaction range is finite but long compared to the interparticle spacing for a range of temperature.