# On the decay of the pair correlation function and the line of vanishing excess isothermal compressibility in simple fluids

## TL;DR

This paper investigates how the decay of pair correlations in simple fluids relates to phase behavior, introducing a new thermodynamic criterion that approximates the Fisher-Widom line by examining the isothermal compressibility.

## Contribution

It proposes a new thermodynamic criterion based on the isothermal compressibility to approximate the Fisher-Widom line in simple fluids, connecting structural decay and phase transitions.

## Key findings

- The new criterion closely matches the Fisher-Widom line in studied models.
- Decay of correlations switches from exponential to oscillatory at the FW line.
- Distinction between true and Ornstein-Zernike correlation lengths is emphasized.

## Abstract

We re-visit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties as manifest in pair correlation functions. We focus on the asymptotic decay of the total correlation function $h(r)$ which is, in turn, controlled by the form of the pair direct correlation function $c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagram into two regions characterized by the two different types of asymptotic decay. We show that there is a new and physically intuitive thermodynamic criterion which approximates well the actual FW line. This new criterion defines a line where the isothermal compressibility takes its ideal gas value $\chi_T=\chi_T^\text{id}$. We test our hypothesis by considering four commonly used models for simple fluids. In all cases the new criterion yields a line in the phase diagram that is close to the actual FW line for the thermodynamic state points that are most relevant. We also investigate (Widom) lines of maximal correlation length, emphasizing the importance of distinguishing between the true and Ornstein-Zernike correlation lengths