Finite-Size Effects and Critical Behavior of the Deconfinement Phase Transition

Abstract

We study the finite-size effects on the deconfinement phase transition (DPT) of hot and / or dense hadronic matter, using a simple thermodynamic model based on the assumption of coexistence of confined and deconfined phases in a finite volume, with the two-phases matter Equations of State. For the QGP, we consider a partition function (PF) with the exact color-singletness requirement. A problem arises in the limit of small QGP volumes when using the usual color-singlet partition function (CSPF) derived in the saddle point approximation. To avoid the problem, we have then proposed a method for calculating a suitable CSPF, which allows us to accurately calculate physical quantities describing well the DPT at finite volumes. We show that in the limit of infinite volume, these thermodynamic quantities exhibit a discontinuity at a critical point Tc(infinity) (or muc(infinity)). In a finite size system, all singularities are smoothed out over a broadened critical region, shifted from the critical point position in the thermodynamic limit. The first derivatives of these thermodynamic quantities show delta function singularities at the critical point in the thermodynamic limit, while in a finite volume, these delta singularities are smeared into finite peaks of widths deltaT(V) (or deltamu(V)), with the maxima of the peaks occuring at pseudo-critical points Tc(V) (or muc(V)). An analysis of the finite size scaling behavior at criticality of these maxima as well as of the width of the transition region and the shift of the critical point allows us to determine the critical exponents characterizing the DPT. Our results are in good agreement with those predicted by other studies for a first-order phase transition.