  Starting from the second equilibrium equation in the BBGKY hierarchy under
the Kirkwood superposition closure, we implement a new method for studying the
asymptotic decay of correlations in the hard disk fluid in the high density
regime. From our analysis and complementary numerical studies, we find that
exponentially damped oscillations can occur only up to a packing fraction
{\eta}*~0.718, a value which is in substantial agreement with the packing
fraction, {\eta}~0.723, believed to characterize the transition from the
ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo
simulations [Phys. Rev. E 73, 065104 (2006)]. We next show that the same method
of analysis predicts that exponential damping of oscillations in the hard
sphere fluid becomes impossible when \lambda = 4n\pi {\sigma}^3 [1 + H(1)]>/-
34.81, where H(1) is the contact value of the correlation function, n is the
number density and {\sigma} is the sphere diameter, in exact agreement with the
condition, \lambda >/- 34.8, first reported in a numerical study of the
Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally,
we show that our method confirms the absence of any structural transition in
hard rods for the entire range of densities below close packing.

Statistical Mechanics;Soft Condensed Matter