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 or
der 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.
In order to trace the initial interaction in ultra-relativistic heavy ion collision in all azimuthal directions, two azimuthal multiplicity-correlation patterns -- neighboring and fixed-to-arbitrary angular-bin correlation patterns -- are suggested.
From the simulation of Au + Au collisions at 200 GeV by using the Monte Carlo models RQMD with hadron re-scattering and AMPT with and without string melting, we observe that the correlation patterns change gradually from out-of-plane preferential one to in-plane preferential one when the centrality of collision shifts from central to peripheral, meanwhile the anisotropic collective flow v_2 keeps positive in all cases. This regularity is found to be model and collision energy independent. The physics behind the two opposite trends of correlation patterns, in particular, the presence of out-of-plane correlation patterns at RHIC energy, are discussed.
