Using transfer matrices up to next-nearest-neighbour (NNN) interactions we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers (Fu et al. Soft Matter 2017 13 3296). Here we identify the theoretical basis for this behaviour. In particular we associate kinks in the growth of correlation lengths with eigenvalue crossing and splitting. Understanding the origin of such structural crossovers answers questions raised by earlier studies and thus bridges the gap between theory and simulations for these reference models.
