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

Aldo Procacci
Université fédérale du Minas Gerais (UFMG), Brésil

Date(s) : 19/01/2018   iCal
11 h 00 min - 12 h 00 min

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.



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