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

Abstract

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.

09 pages, 11 Postscript figures

References in corpus (8)

• Phase transitions in quantum chromodynamics
• First and second order transition in frustrated XY systems
• The Phase Transition to the Quark Gluon Plasma: Recent Results from Lattice Calculations
• String Tension and Thermodynamics with Tree Level and Tadpole Improved Actions
• Phase transition of a finite quark-gluon plasma
• Universality and the Deconfinement Phase Transition in SU(2) Lattice Gauge Theory
• Color singlet suppression of quark-gluon plasma formation
• Effect of colour singletness of quark-gluon plasma in quark-hadron phase transition

Cited by in corpus (7)

• Observation of the critical end point in the phase diagram for hot and dense nuclear matter
• Finite volume effects on the chiral phase transition from Dyson-Schwinger equations of QCD
• Centrality dependence of chemical freeze-out parameters from net-proton and net-charge fluctuations using hadron resonance gas model
• Threshold Collision Energy of the QCD Phase Diagram Tricritical Endpoint
• Critical temperature of deconfinement in a constrained space using a bag model at vanishing baryon density
• Finite Volume Cumulant Expansion in QCD-Colorless Plasma
• Effects of fluctuations and color-neutrality in a finite volume