Abstract
Positional ordering of a two-dimensional fluid of hard disks is examined in tubes so narrowthat only nearest neighbor interactions take place. Using the exact transfer-matrix methodthe transverse and longitudinal pressure components and the correlation function aredetermined numerically. Fluid–solid phase transition does not occur even in the widesttube, where the method just loses its exactness, but the appearance of a dramaticchange in the equation of state and the longitudinal correlation function shows thatthe system undergoes a structural change from a fluid to a solid-like order. Thepressure components show that the collisions are dominantly longitudinal at lowdensities, while they are transverse in the vicinity of the close packing density. Thetransverse correlation function shows that the size of solid-like domains growsexponentially with increasing pressure and the correlation length diverges at closepacking. It is possible to find an analytically solvable model by expanding thecontact distance up to first order. The approximate model, which corresponds to asystem of hard parallel rhombuses, behaves very similarly to the system of harddisks.
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