Liquid-gas phase transition for Gibbs point process with Quermass interaction

We prove the existence of a first order phase transition for continuous Gibbs point process in Rd with Quermass interaction. The Hamiltonian we consider is a linear combination of the volume V, the surface measure S and the Euler-Poincaré characteristic χ of a halo of particles (i.e. an union of balls centred at the positions of particles). We show the non-uniqueness of infinite volume Gibbs measures for special values of activity and temperature, provided that the temperature is low enough. Moreover we show the non-differentiability of the pressure at these critical points. Our main tool is an adaptation of the Pirogov-Sinaï-Zahradnik theory for continuous systems with interaction exhibiting a saturation property.