Finite-Size Effects and Scaling for the Thermal QCD Deconfinement Phase Transition within the Exact Color-Singlet Partition Function

We study the finite-size effects for the thermal QCD Deconfinement Phase Transition (DPT), and use a numerical finite size scaling analysis to extract the scaling exponents characterizing its scaling behavior when approaching the thermodynamic limit. For this, we use a simple model of coexistence of hadronic gas and color-singlet Quark Gluon Plasma (QGP) phases in a finite volume. The Color-Singlet Partition Function (CSPF) of the QGP cannot be exactly calculated and is usually derived within the saddle point approximation. When we try to do calculations with such an approximate CSPF, a problem arises in the limit of small temperatures and/or volumes (VT3<<1), requiring then additional approximations if we want to carry out calculations. We propose in this work a new method for an accurate calculation of any quantity of the finite system, without explicitly calculating the CSPF itself and without any approximation. By probing the behavior of some useful thermodynamic response functions on the hole range of temperature, it turns out that in a finite size system, all singularities in the thermodynamic limit are smeared out and the transition point is shifted away. A numerical finite size scaling analysis of the obtained data allows us to determine the scaling exponents of the QCD DPT. Our results expressing the equality between their values and the space dimensionality is a consequence of the singularity characterizing a first order phase transition and agree very well with the predictions of other FSS theoretical approaches and with the results of both lattice QCD and Monte Carlo models calculations.Comment: 09 pages, 11 Postscript figure

Effect of different SU(3) color representations on the nucleation of quark-gluon plasma droplets from a hadronic gas

We study the nucleation of quark-gluon plasma (QGP) droplets from the hadronic gas phase, based on the calculation of the difference in free energy in the QGP and hadronic gas phases. We investigate this difference in free energy by modeling it in different cases, when the surface tension of the QGP bubble is considered or not. We calculate the free energies of both hadronic gas consisting of massive pions and plasma droplet with up, down and strange quarks additionally to gluons, for different SU ≤ft( 3 ıght) color representations of the QGP, namely the color singlet, color octet, and color 27-plet. The behavior of the obtained change in free energy is examined with varying radius of the QGP bubble, and at different temperatures. The effect of the surface contribution on the nucleated bubble is also investigated and compared to the case without this contribution

An approach to the study of the thermally driven deconfinement phase transition in a finite volume through the order parameter, its derivatives, and cumulants of the probability distribution

We describe the temperature driven deconfining phase transition between hadronic and quark–gluon plasma (QGP) phases coexisting in a finite volume by means of a probability distribution using a simple thermodynamic model. The equations of state of both phases are calculated, where the colour singletness requirement is considered for the QGP phase with massless up and down quarks. We emphasize in this work the probability distribution and try to deeply analyze it to extract information about the transition. Also, the mean values of some response functions, which are mainly the order parameter, its three first thermal derivatives, and the second, third, and fourth cumulants of the probability distribution, are calculated and their behavior with temperature at vanishing chemical potential and at different volumes is examined. The striking result is the large similarity noted between the behavior of the order parameter derivatives and that of their homologous cumulants of the probability density. This similarity is worked out, and particularly the linearity between the thermal susceptibility and the variance is probed.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author