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The analytical canonical NLT partition function of a quasi-one dimensional(q1D) system of hard disks [J. Chem Phys. v.153, 144111 (2020)] provides adirect 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 infinitesystems. It is alternative to the well-developed transfer matrix method basedon the isobaric NPT ensemble. We derive the analytical formulae for the actualdistance dependence of the translational pair distribution function (PDF) andthe DF of distances between next neighbor disks, and then demonstrate their useby calculating the translational order in the pore. In all cases, the order isfound to be of a short range and to exponentially decay with the disks'separation. The correlation length presented for the whole range of the q1Dpore widths and different densities shows a non-monotonic dependence with amaximum at the density N/L=1 and tends to the 1D value for a vanishing porewidth. The results indicate a special role of this density when the pore lengthL is equal exactly to N disk diameters. We introduce an orientational orderparameter that accounts for the local quality of the crystalline zigzag formedby disks and is related to its structural element. This parameter is maximum inthe densely packed state and vanishes for a very low density. Due to specificquasi-one dimensional geometry, this macroscopic order parameter is constantalong the pore so that the macroscopic orientational order is of a liquidcrystalline type.

Correlation functions and ordering in a quasi-one dimensional system of hard disks from the exact canonical partition function