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 \ensuremath{\Gamma}. 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, \ensuremath{\Gamma}\ensuremath{\rightarrow}\ensuremath{\infty} (``Onsager'') limit of the HNC integral equation, and (3) the freezing density of simple liquids.
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