Universality in the jamming limit for elongated hard particles in one dimension

We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are studied (by transfer matrix method) as a function of density and aspect ratio. The behavior in the extreme high-density (jamming) limit is described by a few universality classes depending on the object's shape. In particular, there is a diverging correlation length when the contact point of adjacent objects is far from the line along which their centers move, as for needles and rectangles.