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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 (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. © 2016, Springer Science+Business Media Dordrecht.

Registro:

Documento: Artículo
Título:Convergence of Mayer and Virial expansions and the Penrose tree-graph identity
Autor:Procacci, A.; Yuhjtman, S.A.
Filiación:Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Classical continuous gas; Mayer series; Tree-graph identities
Año:2017
Volumen:107
Número:1
Página de inicio:31
Página de fin:46
DOI: http://dx.doi.org/10.1007/s11005-016-0918-7
Título revista:Letters in Mathematical Physics
Título revista abreviado:Lett. Math. Phys.
ISSN:03779017
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03779017_v107_n1_p31_Procacci

Referencias:

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  • Brydges, D., Martin, P.A., Coulomb systems at low density: a review (1999) J. Stat. Phys., 96, pp. 1163-1330
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  • Fernández, R., Procacci, A., Cluster expansion for abstract polymer models. New bounds from an old approach (2007) Commun. Math. Phys., 274, pp. 123-140
  • Gallavotti, G., (1999) Statistical Mechanics: A Short Treatise, , Springer, New York
  • Groeneveld, J., Estimation methods for Mayer graphical expansions, Doctors thesis published in Proceedings of the Koninklijke Nederlandse Akademie vanWetenschappen, Series 70 (1967) Nrs. 4 and, 5, pp. 451-507
  • Lebowitz, J.L., Penrose, O., Convergence of Virial Expansions (1964) J. Math. Phys., 7, pp. 841-847
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  • de Lima, B.N.B., Procacci, A., The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius (2014) J. Stat. Phys., 157 (3), pp. 422-435
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  • Mayer, J.E., Mayer, M.G., (1940) Statistical Mechanics, , Wiley, New York
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  • Ruelle, D., (1969) Statistical Mechanics: Rigorous Results, , W. A. Benjamin Inc., New York-Amsterdam
  • Ruelle, D., Correlation functions of classical gases (1963) Ann. Phys., 5, pp. 109-120
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Citas:

---------- APA ----------
Procacci, A. & Yuhjtman, S.A. (2017) . Convergence of Mayer and Virial expansions and the Penrose tree-graph identity. Letters in Mathematical Physics, 107(1), 31-46.
http://dx.doi.org/10.1007/s11005-016-0918-7
---------- CHICAGO ----------
Procacci, A., Yuhjtman, S.A. "Convergence of Mayer and Virial expansions and the Penrose tree-graph identity" . Letters in Mathematical Physics 107, no. 1 (2017) : 31-46.
http://dx.doi.org/10.1007/s11005-016-0918-7
---------- MLA ----------
Procacci, A., Yuhjtman, S.A. "Convergence of Mayer and Virial expansions and the Penrose tree-graph identity" . Letters in Mathematical Physics, vol. 107, no. 1, 2017, pp. 31-46.
http://dx.doi.org/10.1007/s11005-016-0918-7
---------- VANCOUVER ----------
Procacci, A., Yuhjtman, S.A. Convergence of Mayer and Virial expansions and the Penrose tree-graph identity. Lett. Math. Phys. 2017;107(1):31-46.
http://dx.doi.org/10.1007/s11005-016-0918-7