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We analyze a generalization of the hard sphere dipole system in twodimensions in which the interaction range of the interaction can be varied. Wefocus on the system in the limit the interaction becomes increasinglyshort-ranged, while the temperature becomes low. By using a cluster expansionand taking advantage of low temperatures to perform saddle-pointapproximations, we argue that a well defined double limit exists in which theonly structures which contribute to the free energy are chains. We then arguethat the dominance of chain structures is equivalent to the dominance of chaindiagrams in a cluster expansion, but only if the expansion is performed arounda hard sphere system (rather than the standard ideal gas). We show that thisleads to non-standard factorization rules for diagrams, and use this toconstruct a closed-form expression for the free energy at low densities. Wethen compare this construction to several models previously developed for thehard sphere dipole system in the regime where chain structures dominate, andargue that the comparison provides evidence in favor of one model over theothers. We also use this construction to incorporate some finite densityeffects though the hard sphere radial distribution function, and analyze theimpact of these effects on chain length and the equation of state.

Chain Formation in a 2-Dimensional System of Hard Spheres with a Short Range, Anisotropic Interaction