Application of Mayer'S Theory to the Study of One Dimensional Systems with Repulsive and Weak, Long Range Interactions

摘要

Mayer's theory is applied to systems with infinitely repulsive (hard rod) and weak, long range pair potentials. Infinite sets of irreducible integrals are found analytically for each case. A theorem on star graph degeneracies is derived from the hard rods solution. The addition of weak attraction to hard repulsion is shown to give rise to a van der Waals equation of state. When a cluster-width dependent potential is examined, it is found that a region of relatively soft repulsion acts like a weak attraction. (Author)