Fixed point behavior of cumulants in the three-dimensional Ising universality class

TL;DR

This study investigates the fixed point behavior of high-order cumulants in the 3D Ising model, revealing temperature and energy independence at criticality, which has implications for understanding QCD critical dynamics in heavy-ion collisions.

Contribution

It demonstrates the fixed point behavior of normalized cumulants in the 3D Ising model at critical temperature and extends this finding to finite systems and QCD-related energy dependence.

Findings

Normalized cumulants are independent of magnetic field at critical temperature.

Fixed point behavior persists in finite-size Monte Carlo simulations.

Fixed point behavior observed in energy dependence along freeze-out curves.

Abstract

High-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class with the Quantum chromo-dynamics, temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated by Monte Carlo method, the fixed point behavior still exists at the temperature near the critical one. The fixed point behavior is also appeared in the temperature dependence of normalized factorial cumulants at least from the fourth-order one. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.