Fixed point behavior mapping of cumulants between the three-dimensional Ising model and QCD

TL;DR

This paper investigates how the fixed point behavior of normalized cumulants in the 3D Ising model relates to QCD critical phenomena, considering the effects of mapping parameters on experimental observables near the QCD critical point.

Contribution

It analyzes the impact of non-universal mapping parameters on the fixed point behavior of cumulants in the QCD critical point context, extending previous Ising model results.

Findings

Fixed point behavior persists when Ising variables are orthogonal after mapping.

The fixed point is closer to the QCD critical point than the cumulant peaks.

Mapping parameters significantly influence the fixed point's location.

Abstract

Fixed point behavior was found in the temperature dependence of normalized cumulants of order parameter at different external magnetic fields in the three-dimensional Ising model in my last work. In this paper, considering possible existing QCD critical point belonging to the three-dimensional Ising universality class and the non-universal mapping parameters between the Ising model and QCD, effects of the mapping parameters on the fixed point behavior in the net-baryon chemical potential dependence of normalized cumulants along different experimental freeze-out curves is studied in this paper. We found that when the directions of Ising variables, the reduced temperature and external magnetic field, are orthogonal or not far from orthogonal after mapping to the QCD temperature and net-baryon chemical potential plane, the fixed point behavior exists in the net-baryon chemical potential dependence of the normalized cumulants and is closer to the QCD critical point than the peak in the cumulants.