Partition Function for a Generalized Tonks' Gas

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Abstract
The partition function of a system of N identical rigid rods connected by identical springs is reduced to a onefold integration. This integration is explicitly performed in the limit N → ∞ by the method of steepest descent. The system behaves respectively as a gas and as a solid in two different limiting cases. The calculated isotherms and specific heat show that the transition between these limiting cases is continuous.

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