The Experimental Detection Method Of The Second Oder Phase Transition Critical Point And The First Phase Boundary In The Finite System

According to the big bang theory, the material world was composed by a quark-gluon plasma at the beginning of the formation of the universe. In1970s, T.D.Lee et al predicted by relativistic heavy-ion collision experiments we can produce high-temperature and high-density environment making the hadron matter changes, resulting quark-gluon plasma.From the beginning of the1980s, international physicists have conducted a series of relativistic heavy-ion collision experiments. The purpose is to study the phase diagram of strong interaction phase transition and to find the critical point and the phase boundary. The study found that the ratios of higher cumulants of conserved quantities (such as net baryon number, net charge and net strangeness) distributions are sensitive to the QCD phase transition. They may have the non-monotonic behavior or sign modifications. Thus, high cumulants are an important observable to explore the critical point of QCD phase transition.But in the relativistic heavy ion collision experiments, as the scale and the evolution time of the system is finite, the system cannot reach infinity. The space-time scales the set the dynamics of the quark-gluon plasma formed in relativistic heavy ion collisions differ from the cosmological ones by almost20orders of magnitude. For the finite system, the correlation length is trivially bounded by the finite volume and, through causality, by the finite lifetime of the system. It is finite at the critical point. All signatures of the critical endpoint based on non-monotonic behavior or sign change will probe a pseudocritical endpoint, shifted from the critical point in the thermodynamic limit. In this paper we point out that the finite-size effect is not negligible in locating critical point of QCD phase transition at current relativistic heavy ion collisions.For the finite system, it has finite size scaling behavior in the vicinity of the critical point. The scaling function is a constant at the critical temperature. For different system sizes, the curves of the scaling critical related observables vs temperature will intersect to one point at critical temperature. This point is called fixed point. If we can find the fixed point, we can get the critical temperature.How can we find the fixed point? We define a quantity, D, which can quantitatively describe the point liked behavior. For the relativistic heavy ion collision system, the curves will not intersect to one point because of the experimental error. In fact, at the critical temperature, the scaling critical related observables of different system sizes obey the normal distribution. Then if the value of D is around1, we say that there is a fixed point. We give a method to determine the critical temperature, the critical exponent and the order of the phase transition through the quantity D.We use two dimensional Ising model and three dimensional three-state Potts model the phase transition of which are the second order and the first order phase transition respectively as an example to verify the feasibility of this method. From the result model of the model, we find that the narrower the width of the point distribution, the smaller value of D, which will closer to1. And the value of D is sensitive to the fixed point. When the width of the point distribution slightly increases a little, the value of D will increase a lot. This method has an important reference value and guidance for finding the QCD critical point and phase boundary.