Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

TL;DR

This study investigates the behavior of the sixth order cumulant of the order parameter in the 3D Ising model, revealing finite-size effects and sign change characteristics relevant to QCD critical point searches.

Contribution

It provides a theoretical analysis of the sixth order cumulant's temperature dependence and finite-size effects within the 3D Ising universality class, connecting to QCD critical phenomena.

Findings

Negative valley in the sixth order cumulant near the critical point

Width of the negative valley decreases with external magnetic field

Finite-size effects shift the sign change temperature

Abstract

The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign.