# Comparison of two efficient methods for calculating partition functions

## TL;DR

This paper compares a new direct integral method with nested sampling for calculating partition functions, demonstrating that the new approach is significantly faster and more precise in solid argon simulations.

## Contribution

The paper introduces a direct integral approach that outperforms nested sampling in speed and accuracy for partition function calculations.

## Key findings

- The new method is at least four orders faster than nested sampling.
- The direct integral approach achieves about 10 times higher precision.
- Results agree well with molecular dynamics and experimental data.

## Abstract

In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral approach that works at least four orders faster. In present work, the above two methods were applied to solid argon at temperatures up to $300$K, and the derived internal energy and pressure were compared with the molecular dynamics simulation as well as experimental measurements, showing that the calculation precision of our approach is about 10 times higher than that of the nested sampling method.