  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.
