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-order 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 generic features of the cumulants are discussed. They are instructive to the high-order cumulants of the net baryon number in the QCD ph...
