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In this article we obtain a fundamental measure functional for the model ofaligned hard hexagons in the plane. Our aim is not just to provide a functionalfor a new, admittedly academic, model, but to investigate the structure offundamental measure theory. A model of aligned hard hexagons has similaritieswith the hard disk model. Both share "lost cases", i.e. admit configurations ofthree particles in which there is pairwise overlap but not triple overlap.These configurations are known to be problematic for fundamental measurefunctionals, which are not able to capture their contribution correctly. Thisfailure lies in the inability of these functionals to yield a correct lowdensity limit of the third order direct correlation function. Here we derivethe functional by projecting aligned hard cubes on the plane x+y+z=0. Thecorrect dimensional crossover behavior of these functionals permits us tofollow this strategy. The functional of aligned hard cubes, however, does nothave lost cases, so neither had the resulting functional for aligned hardhexagons. The latter exhibits, in fact, a peculiar structure as compared to theone for hard disks. It depends on a uniparametric family of weighted densitiesthrough a new term not appearing in the functional for hard disks. Apart fromstudying the freezing of this system, we discuss the implications of thefunctional structure for new developments of fundamental measure theory.

Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory