Inflection point as a characteristic of the QCD critical point

TL;DR

This paper explores the relationship between inflection points in the equation of state and high cumulants of conserved quantities as indicators of the QCD critical point, demonstrating their correlation across different physical systems.

Contribution

It establishes a general connection between inflection points in the EoS and sign changes in high cumulants, proposing combined measurements to identify the QCD critical point.

Findings

Inflection points in EoS correlate with sign changes in high cumulants.

The relationship holds across fluid, spin models, and QCD matter.

Measuring EoS and cumulants together aids in locating the QCD critical point.

Abstract

The appearance of the inflection point in the equation of state (EoS) is associated with the second order phase transition. The high cumulants of conserved quantities near the critical point are corresponding to the high derivatives of the EoS near the inflection point. The critical behavior of high cumulants of conserved charge near the QCD critical point, in particular, the sign change, is closely related to the appearance of inflection point. We show in general how the times of sign change of high cumulants relate to the order of derivative. We also demonstrate that the character of inflection point of EoS is as visible as the sign change of high cumulants in 3 systems, i.e., van der Waals equation of fluid, magnetization of spin models and the baryon number density of QCD matter. Therefore, we propose that the EoS, or the mean of baryon number density, should be measured and studied together with its higher cumulants in exploring QCD critical point in heavy ion collisions.