Physics

Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite volume transition point T0(V ) of the QCD deconfinement phase transition to a Colorless QGP, we have developed a new approach using the finite size cumulant expansion of the order parameter and the Lmn-method. The first six cumulants C1,2,3,4,5,6 with the corresponding under-normalized ratios(skewness Σ, kurtosis κ ,pentosis Π± and hexosis H1,2,3) and three unnormalized combinations of them (O = σ 2 κΣ −1 , U = σ −2 Σ −1 , N = σ 2 κ) are calculated and studied as functions of (T, V ). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite volume transition point. The extracted transition temperature value T0(V ) agrees with that expected T N 0 (V ) from the order parameter and the thermal susceptibility χT (T, V ), according to the standard procedure of localization to within about 2%. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.