Critical fluctuations in models with van der Waals interactions

TL;DR

This paper investigates particle number fluctuations in the van der Waals model, revealing critical behavior and singularities near the critical point, with implications for understanding the QCD critical point.

Contribution

It provides a detailed analysis of fluctuations within the VDW model, including new insights into strongly intensive measures near criticality.

Findings

Fluctuations exhibit singular behavior near the critical point.

The measure $ ext{Δ}[E^*,N]$ can be both positive and negative near criticality.

Similar fluctuation patterns are expected near the QCD critical point.

Abstract

Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions. The VDW equation is used to calculate the scaled variance of particle number fluctuations in generic Boltzmann VDW system and in nuclear matter. The strongly intensive measures $\Delta[E^*,N]$ and $\Sigma[E^*,N]$ of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the critical point. The $\Delta[E^*,N]$ measure is shown to attain both positive and negative values in the vicinity of critical point. Based on universality argument, similar behavior is expected to occur in the vicinity of the QCD critical point.