Abstract
The partition function of the classical one-dimensional hard rod fluid with a residual long range interaction can be evaluated exactly, with the aid of an auxiliary field, in the limit where the range of the potential goes to infinity. If the Fourier spectrum of the residual interaction lacks components at finite wave vector, the infinite range limit recovers the celebrated result of the Kac-Uhlenbeck-Hemmer model of condensation. Otherwise, it predicts a continuous second-order freezing transition.
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