  The high-order cumulants and factorial cumulants of conserved charges are
suggested to study the critical dynamics in heavy ion collisions. In this
paper, using parametric representation of the 3-dimensional Ising model, the
sign distribution on the phase diagram and temperature dependence of the
cumulants and factorial cumulants is studied and compared. In the vicinity of
the critical point, the cumulants and factorial cumulants can not be
distinguished. Far away from the critical point, sign changes occur in the
factorial cumulants comparing with the same order cumulants. The cause of these
sign changes is analysed. They may be used to measure the distance to the
critical point.
