  Considering different universality classes of the QCD phase transitions, we
perform the Monte Carlo simulations of the 3-dimensional $O(1, 2, 4)$ models at
vanishing and non-vanishing external field, respectively. Interesting high
cumulants of the order parameter and energy from O(1) (Ising) spin model, and
the cumulants of the energy from O(2) and O(4) spin models are presented. The
critical features of the cumulants are discussed. They are instructive to the
high cumulants of the net baryon number in the QCD phase transitions.
