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

Abstract

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 and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in 1964 for the Virial series. To get our results we exploit the tree-graph identity given by Penrose in 1967 using a new partition scheme based on minumum spanning trees.

Final version, to be published in Letters in Mathematical Physics

References in corpus (5)

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Cited by in corpus (8)

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• Absolute convergence of the free energy of the BEG model in the disordered region for all temperatures
• On the Mayer series of two-dimensional Yukawa gas at inverse temperature in the interval of collapse
• Cluster expansion for the Ising model in the canonical ensemble
• Analyticity for locally stable hard-core gases via recursion