Finite-size effects and scaling for the thermal QCD deconfinementphase transition within the exact color-singlet partition function

Abstract.

We study the finite-size effects for the thermal quantum chromodynamics (QCD) deconfinement phase transition, and use a numerical finite-size scaling analysis to extract the scaling exponents characterizing its scaling behavior when approaching the thermodynamic limit $\left(V\longrightarrow \infty \right)$. 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 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 color-singlet partition function, a problem arises in the limit of small temperatures and/or volumes $VT^{3} < < 1$, requiring additional approximations if we want to carry out calculations. We propose in this work a method for an accurate calculation of any quantity of the finite system, without any approximation. By probing the behavior of some useful thermodynamic response functions on the whole 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 (FSS) analysis of the obtained data allows us to determine the scaling exponents of the QCD deconfinement phase transition. 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 to a first-order phase transition and with the results of calculations using Monte Carlo methods in both lattice QCD and statistical physics models.