Mayer and Virial Series at Low Temperature

We analyze the Mayer and virial series (pressure as a function of the activity resp. the density) for a classical system of particles in continuous configuration space at low temperature. Particles interact via a finite range potential with an attractive tail. We propose physical interpretations of the Mayer and virial series’ radii of convergence, valid independently of the question of phase transition: the Mayer radius corresponds to a fast increase from very small to finite density, and the virial radius corresponds to a cross-over from monatomic to polyatomic gas. Our results are consistent with the Lee-Yang theorem for lattice gases and with the continuum Widom-Rowlinson model.