Extension of the Uhlenbeck-Ford Model with an Attraction

TL;DR

This paper extends the Uhlenbeck-Ford model by adding an attractive component, enabling analytical calculation of virial coefficients up to sixth order and linking it to common potentials like Lennard-Jones.

Contribution

It introduces an analytically tractable extension of the Uhlenbeck-Ford model with attraction, facilitating calculations of higher-order virial coefficients.

Findings

Virial coefficients calculated up to order 6.

Reduced graph integrals to a combinatorial problem.

Established connection to Lennard-Jones potential.

Abstract

The Uhlenbeck-Ford model for soft repulsion, which has only a repulsive interaction, is extended by inclusion of an attraction. This extension still allows an analytical evaluation of the virial coefficients. The integrals over the graph contributions are reduced to a combinatorial problem. We have calculated the virial coefficients to order 6 in the density. A link is made between this model and more common interactions, like the 12-6 Lennard-Jones potential.