Existence and nature of a freezing transition inside three-dimensional arrays of narrow channels

The density functional for matter confined inside a three-dimensional array of narrow channels is constructed. It is shown that the effect of long range interactions amounts to a three-dimensional quadratic perturbation on an array of one-dimensional hard rods. Hence, it follows that the recently proposed freezing transition of atoms confined in nanotube arrays is continuous. This conclusion is validated beyond mean field theory by Monte Carlo simulations in the NPT ensemble.