Convergence of the iterative process for the diagrammatic expansion as related to liquid structure and freezing

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Abstract
The stability of the solution of the hypernetted-chain (HNC) integral equation for the pair-correlation function of the fluid, with respect to its defining diagrammatic iteration loop, is investigated in one, two, and three dimensions for the inverse-power potentials characterized by a single dimensionless coupling parameter Γ. The Onsager limit and the solution of the HNC equation belong to the same basin of attraction with respect to the diagrammatic iterative map. A connection is established between (1) convergence properties of the diagrammatic low-density Mayer expansion, (2) the asymptotic strong-coupling, Γ→∞ (‘‘Onsager’’) limit of the HNC integral equation, and (3) the freezing density of simple liquids.