Liquid pair correlations in four spatial dimensions: Theory versus simulation

TL;DR

This paper compares theoretical predictions and simulation data for particle pair correlations in four-dimensional liquids, providing insights into high-dimensional crystal and glass formation.

Contribution

It evaluates various closure relations for the Ornstein-Zernike equation in 4D and compares them with simulation results, advancing high-dimensional liquid theory.

Findings

Different closures show varying accuracy in predicting pair correlations.

Simulation data validates some theoretical approaches over others.

Results inform understanding of high-dimensional phase transitions.

Abstract

Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the Ornstein-Zernike equation, by comparing the results to computer simulation data. Our results are of relevance to understand crystal and glass formation in high-dimensional systems.