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

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.