Structural transitions in hypersphere fluids: predictions of Kirkwood's approximation

TL;DR

This paper predicts phase transitions in hypersphere fluids across dimensions 3 to 6 using an analytic criterion based on Kirkwood's superposition approximation, aligning qualitatively with numerical results.

Contribution

It introduces an analytic approach to determine structural transition thresholds in high-dimensional hard sphere systems using Kirkwood's approximation.

Findings

Predicts phase transition thresholds in D=3 to 6 dimensions.

Derives asymptotic conditions for D approaching infinity.

Shows qualitative agreement with numerical studies.

Abstract

We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D=3,4,5 and 6, proceeding from the YBG hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurence of a structural transition in the D->Infinity limit .