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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.
High-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy ion collisions. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belon
We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by the event-by-event analysis in relativistic heavy-ion collisions. After defining the factorial cumulants for systems wi
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
We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately
In this work we study the temperature dependence of the equilibrium variance of critical fluctuations near the QCD critical point. In particular, we take the finite size of the fireball created in heavy-ion collisions into account and systematically