One-Dimensional Gases with Hard-Core Repulsion

Abstract

An elementary mathematical device previously employed to derive the statistical mechanical properties of a classical one-dimensional gas with interaction potential that satisfies a linear differential equation with constant coefficients over the domain (0, ∞) is shown to be also applicable when the potential contains a repulsive hard core. In particular, the thermodynamic properties of a one-dimensional plasma of hard rods and of the gas model of Kac are derived. The infinite-range phase transition obtained in the latter case by Kac, Uhlenbeck, and Hemmer is found to be amenable to investigation by the methods used.