  The analytical canonical NLT partition function of a quasi-one dimensional
(q1D) system of hard disks [J. Chem Phys. v.153, 144111 (2020)] provides a
direct analytical description of the thermodynamics and ordering in this system
(a pore) as a function of the linear density N/L both for finite and infinite
systems. It is alternative to the well-developed transfer matrix method based
on the isobaric NPT ensemble. We derive the analytical formulae for the actual
distance dependence of the translational pair distribution function (PDF) and
the DF of distances between next neighbor disks, and then demonstrate their use
by calculating the translational order in the pore. In all cases, the order is
found to be of a short range and to exponentially decay with the disks'
separation. The correlation length presented for the whole range of the q1D
pore widths and different densities shows a non-monotonic dependence with a
maximum at the density N/L=1 and tends to the 1D value for a vanishing pore
width. The results indicate a special role of this density when the pore length
L is equal exactly to N disk diameters. We introduce an orientational order
parameter that accounts for the local quality of the crystalline zigzag formed
by disks and is related to its structural element. This parameter is maximum in
the densely packed state and vanishes for a very low density. Due to specific
quasi-one dimensional geometry, this macroscopic order parameter is constant
along the pore so that the macroscopic orientational order is of a liquid
crystalline type.
