THE STRUCTURE OF DENSITY FUNCTIONALS

The density functional format for classical fluids in thermal equilibr ium has the joint virtues of simplicity and reasonable accuracy, but t he drawback that ignorance of its basic structure makes systematic imp rovement difficult. It seems clear that incorporation of auxiliary den sities plays an important role, but their genesis is not well understo od. A sequence of increasingly complex lattice models has been set up and solved in order to probe this question. The Bethe lattice translat es to a modified mean field continuum free energy functional, while th e introduction of rudimentary non-simple connectivity results in an ef fective but complex integral equation form. In either case, of their e xtensions, there is evidence that the underlying model represents no r eal system, even with multi-body interactions, and it is suggested tha t what is missing in the description is the effect of non-local collec tive amplitudes.