Analytical canonical partition function of a quasi-one dimensional system of hard disks

The exact canonical partition function of a hard disk system in a narrow quasi-one dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result the many body problem is reduced to solving two transcendental equations which can be easily done numerically. The longitudinal and transverse pressures in the whole density range are presented for three different pore widths. The transition from the solidlike zigzag to the liquidlike state is found to be quite sharp in the density scale but shows no genuine singularity. This transition is quantitatively described by the distribution of zigzag’s windows through which disks exchange their positions across the pore.