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The canonical $\,NLT\,$ partition function of a quasi-one dimensional (q1D)one-file system of equal hard disks [J. Chem Phys. \textbf{153}, 144111 (2020)]provides an analytical description of the thermodynamics and ordering in thissystem (a pore) as a function of linear density $\,Nd/L\,$ where $\,d\,$ is thedisk diameter. We derive the analytical formulae for the distance dependence ofthe translational pair distribution function and the distribution function ofdistances between next neighbor disks, and then demonstrate their use bycalculating 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 different pore widths anddensities shows a non-monotonic dependence with a maximum at $\,Nd/L = 1\,$ andtends to the 1D value for a vanishing pore width. The results indicate aspecial role of this density when the pore length $\,L\,$ is equal exactly to$N$ disk diameters. A comparison between the theoretical results for aninfinite system and the results of a molecular dynamics simulation for a finitesystem with periodic boundary conditions is presented and discussed.

Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks