The structure of density functionals

The density functional format for classical fluids in thermal equilibrium has the joint virtues of simplicity and reasonable accuracy, but the drawback that ignorance of its basic structure makes systematic improvement difficult. It seems clear that incorporation of auxiliary densities plays an important role, but their genesis is not well understood. A sequence of increasingly complex lattice models has been set up and solved in order to probe this question. The Bethe lattice translates to a modified mean field continuum free energy functional, while the introduction of rudimentary non-simple connectivity results in an effective but complex integral equation form. In either case, or their extensions, there is evidence that the underlying model represents no real system, even with multi-body interactions, and it is suggested that what is missing in the description is the effect of non-local collective amplitudes.