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Convergence of density expansions of correlation functions and the Ornstein-Zernike equation

Kuna, T. and Tsagkarogiannis, D. (2018) Convergence of density expansions of correlation functions and the Ornstein-Zernike equation. Annales Henri Poincare, 19 (4). pp. 1115-1150. ISSN 1424-0661

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To link to this item DOI: 10.1007/s00023-018-0655-9


We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation.

Item Type:Article
Divisions:Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE)
Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:74828
Publisher:Springer International Publishing


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