Journal of Statistical Physics

, Volume 147, Issue 4, pp 678–706 | Cite as

Mayer and Virial Series at Low Temperature

  • Sabine JansenEmail author


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.


Classical statistical mechanics Mayer and virial series Phase transitions 



The author gratefully acknowledges very useful discussion with D. Ueltschi, D. Tsagkarogiannis, E. Presutti, E. Pulvirenti, B. Metzger and W. König, and also thanks E. Presutti for hospitality during a visit at the University of Rome “Tor Vergata”. This work was supported by the DFG Forschergruppe 718 “Analysis and stochastics in complex physical systems”.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e.V.BerlinGermany

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