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

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system equal hard disks Pergamenshchik [19] provides an analytical description the thermodynamics and ordering in this (a pore) as linear density Nd/L where d is disk diameter. We derive formulae for distance dependence translational pair distribution distances between next neighbor disks, then demonstrate their use by calculating order pore. In all cases, found to be short range exponentially decay with disks' separation. correlation length presented different pore widths densities shows non-monotonic maximum at Nd/L=1 tends 1D value vanishing width. results indicate special role when L exactly N diameters. Comparison theoretical infinite molecular dynamics simulation finite periodic boundary conditions discussed.