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Tate, Stephen James (2013) Virial expansion bounds. Journal of Statistical Physics, Volume 153 (Number 2). pp. 325-338. doi:10.1007/s10955-013-0831-8 ISSN 0022-4715.
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Official URL: http://dx.doi.org/10.1007/s10955-013-0831-8
Abstract
In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129–183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Journal of Statistical Physics | ||||||
Publisher: | Springer New York LLC | ||||||
ISSN: | 0022-4715 | ||||||
Official Date: | October 2013 | ||||||
Dates: |
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Volume: | Volume 153 | ||||||
Number: | Number 2 | ||||||
Page Range: | pp. 325-338 | ||||||
DOI: | 10.1007/s10955-013-0831-8 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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