We test the performance of a recently proposed fundamental measure density
functional of aligned hard cylinders by calculating the phase diagram of a
monodisperse fluid of these particles. We consider all possible liquid
crystalline symmetries, namely nematic, smectic and columnar, as well as the
crystalline phase. For this purpose we introduce a Gaussian parameterization of
the density profile and use it to minimize numerically the functional. We also
determine, from the analytic expression for the structure factor of the uniform
fluid, the bifurcation points from the nematic to the smectic and columnar
phases. The equation of state, as obtained from functional minimization, is
compared to the available Monte Carlo simulation. The agreement is is very
good, nearly perfect in the description of the inhomogeneous phases. The
columnar phase is found to be metastable with respect to the smectic or crystal
phases, its free energy though being very close to that of the stable phases.
This result justifies the observation of a window of stability of the columnar
phase in some simulations, which disappears as the size of the system
increases. The only important deviation between theory and simulations shows up
in the location of the nematic-smectic transition. This is the common drawback
of any fundamental measure functional of describing the uniform phase just with
the accuracy of scaled particle theory.Comment: 17 pages, 5 figure