Seminarium Fizyki Materii Skondensowanej

A short presentation of the Kirkwood superposition approximationleading to a closure of the equilibrium YBG hierarchy will be followedby an analysis of the resulting asymptotic decay of correlations. Itwill be shown that in the case of hard discs, hard spheres, and hardhyperspheres the exponentially damped oscillations characterising thefluid phase become impossible beyond a certain threshold density thusindicating the freezing transition. In an analogous study of a square-well fluid an analytic criterion forthe existence of a liquid-vapor critical point will be presented.However, despite extensive numerical studies the possibility ofsatisfying the derived criterion could not been achieved. The problem hasbeen then solved quite unexpectedly by a simple analytic argument showingthat the generalized compressibility equations ruled out the existence ofa critical point within the Kirkwood superposition approximation.