Equation of State for a Gas with a Weak, Long-Range Positive Potential
- 1 August 1964
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 5 (8), 1153-1157
- https://doi.org/10.1063/1.1704220
Abstract
A one‐dimensional fluid model in which the pair interaction potential is exponential and repulsive is considered, and the equation of state in the ``long‐range'' limit is determined exactly. This model is complementary to one studied by Kac, in which the pair potential consists of a hard core and an exponential, attractive tail. In that model a phase transition occurs, but in the current model there is no phase transition. This fact lends support to a conjecture of Ruelle that no phase transition occurs if the potential is bounded. The possibility of applying the method of Kac to a wider class of potentials is suggested, and some of the mathematical difficulties yet to be overcome are outlined.Keywords
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