Convergence of Mayer and Virial expansions and the Penrose tree-graph identity

We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109–120, 1963) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841–847, 1964) for the Virial series. To get our results, we exploit the tree-graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967) using a new partition scheme based on minimum spanning trees.