Equation of State for a Gas with a Weak, Long-Range Positive Potential

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.