  Positional ordering of a two-dimensional fluid of hard disks is examined in
such narrow tubes where only the nearest-neighbor interactions take place.
Using the exact transfer-matrix method the transverse and longitudinal pressure
components and the correlation function are determined numerically. Fluid-solid
phase transition does not occur even in the widest tube, where the method just
loses its exactness, but the appearance of the dramatic change in the equation
of state and the longitudinal correlation function shows that the system
undergoes a structural change from a fluid to a solid-like order. The pressure
components show that the collisions are dominantly longitudinal at low
densities, while they are transverse in the vicinity of close packing density.
The transverse correlation function shows that the size of solid-like domains
grows exponentially with increasing pressure and the correlation length
diverges at close packing. It is managed to find an analytically solvable model
by expanding the contact distance up to first order. The approximate model,
which corresponds to the system of hard parallel rhombuses, behaves very
similarly to the system of hard disks.
