Cumulants and factorial cumulants in the 3-dimensional Ising universality class

TL;DR

This paper investigates high-order cumulants and factorial cumulants in the 3D Ising model to understand their behavior near critical points, revealing sign changes that could indicate proximity to criticality in heavy ion collisions.

Contribution

It provides a detailed analysis of cumulants and factorial cumulants in the 3D Ising universality class, highlighting their sign behavior and potential as critical point indicators.

Findings

Near the critical point, cumulants and factorial cumulants are indistinguishable.

Far from the critical point, factorial cumulants exhibit sign changes not seen in cumulants.

Sign changes in factorial cumulants can be used to measure the distance to the critical point.

Abstract

The high-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy ion collisions. In this paper, using parametric representation of the 3-dimensional Ising model, the sign distribution on the phase diagram and temperature dependence of the cumulants and factorial cumulants is studied and compared. In the vicinity of the critical point, the cumulants and factorial cumulants can not be distinguished. Far away from the critical point, sign changes occur in the factorial cumulants comparing with the same order cumulants. The cause of these sign changes is analysed. They may be used to measure the distance to the critical point.