High-order cumulants and correlation functions near the critical point from molecular dynamics

TL;DR

This study uses molecular dynamics simulations of Lennard-Jones fluids to analyze high-order particle number fluctuations near the critical point, revealing strong deviations from ideal behavior and effects of finite system size.

Contribution

It extends previous research by examining third- and fourth-order cumulants and correlation functions in both coordinate and momentum space near the critical point.

Findings

Non-Gaussian cumulants equilibrate quickly near the critical point

Strong deviations from ideal gas behavior are observed in cumulants

Efficiency cuts significantly dilute the critical point signals

Abstract

We present a systematic investigation of particle number fluctuations in the crossover region near the critical endpoint of a first-order phase transition using molecular dynamics simulations of the classical Lennard-Jones fluid. We extend our prior studies to third- and fourth-order cumulants in both coordinate- and momentum-space acceptances and integrated correlation functions (factorial cumulants). We find that, even near the critical point, non-Gaussian cumulants equilibrate on time scales comparable to those of the second-order cumulants, but show stronger finite-size effects. The presence of interactions and of the critical point leads to strong deviations of the cumulants from the ideal-gas baseline in coordinate space; these deviations are expected to persist in momentum space in the presence of collective expansion. In particular, the kurtosis becomes strongly negative, $\kappa \sigma^2 \ll -1$, on the crossover side of the critical point. However, this signal is significantly diluted once an efficiency cut used to distinguish protons from baryons is applied, leading to $|\kappa \sigma^2| \lesssim 1$ even in the presence of the critical point. We discuss our results in the context of ongoing measurements of proton number cumulants in heavy-ion collisions in RHIC-BES-II.