A hard disc system; an Ising-like behaviour in a thin layer

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Abstract
The properties of hard discs in a channel (separation D) have been studied for the σ ⪕ D ⪕ 2σ regime (σ = diameter of the discs), since this regime connects the one-dimensional and two-dimensional cases which exhibit very different free energy functions. Both mechanical and computer simulation results clearly show qualitatively different states of order at low and high packing densities, respectively. A theoretical analysis of the system is presented utilizing a ‘double line’ model. The predicted variation of defect density versus packing density agrees phenomenologically with the results of the mechanical and computer simulations.