A Toeplitz representation for repulsive systems

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Abstract
A new method is presented for the calculation of thermodynamic properties of ensembles of particles interacting via repulsive forces. A tridiagonal matrix representation is constructed in terms of the cluster integrals. Its asymptotic form is utilised to obtain very good numerical estimates of the thermodynamic properties. Moreover, it is shown that the fluid branch may terminate at a critical activity zc, which is identical to the activity at the fluid-solid transition. A relation is found between zc and the radius of convergence of the activity series via the asymptotic matrix elements.

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