Phase instability and the direct correlation function integral equation

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Abstract
Extensive searches for the equilibrium liquid–solid coexistence line have been based on the identification of this line with the bifurcation points in integral equations such as the lowest order Kirkwood lambda coupling equation, the lowest order Born and Green equation, and a similar relation between the direct correlation function and the singlet density. In applications where these integral equations should be identical, different results have been found. The difference is explained by noting that additional, implicit approximations have always been introduced. A new formulation free of such approximations is given, and it is shown that the general condition for bifurcation to occur is simply expressed in terms of the direct correlation function and has a simple physical interpretation: An approximation free search for bifurcation points will identify points of liquid instability and not points of liquid–solid coexistence.