Mapping a solid onto an ‘‘effective liquid’’

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Abstract
The most notable success of the various density-functional theories of freezing is achieved for hard spheres where the density change upon freezing is relatively large, while they more or less equally fail when applied to soft inverse-power interactions where the density change upon freezing is much smaller. It is argued that this relatively large density change makes the hard-sphere freezing results insensitive to physics details in the density-functional calculational setup. As an example, it is demonstrated that the equations of state for the solid near melting as obtained by all the leading density-functional theories of freezing, in their particularly successful application to the freezing of hard spheres and hard disks, are related by a trivial parabola-shift transformation from the liquid excess free energy onto that for the solid. Conclusions regarding the relative merit of the free-energy functionals, which are based only on their performance for the hard-sphere fluid-solid transition, can be misleading.

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