Calculating and resumming the classical virial expansion using automated algebra

TL;DR

This paper computes virial coefficients for a classical gas using schematic models and demonstrates that Padé-Borel resummation significantly improves the convergence of the virial expansion, especially at strong couplings.

Contribution

It introduces an automated algebra approach to calculate virial coefficients and applies resummation techniques to enhance convergence analysis.

Findings

Virial coefficients calculated up to sixth order.

Padé-Borel resummation improves convergence at strong couplings.

Virial expansion fails to converge at high interaction strengths.

Abstract

Using schematic model potentials, we calculate exactly the virial coefficients of a classical gas up to sixth order and use them to assess the convergence properties of the virial expansion of basic thermodynamic quantities such as pressure, density, and compressibility. At sufficiently strong couplings, as expected, the virial expansion fails to converge. However, at least for the interactions and parameter ranges we explored, we find that Pad\'e-Borel resummation methods are extremely effective in improving the convergence of the expansion.