## Etude des effets de volume de la transition de deconfinement vers un QGP sans couleur

##### Abstract

This thesis deals with the deconfinement phase transition of a , using a
simple model of coexisting hadron and QGP phases in a finite volumefi The equations of
state of infinite matter of the two phases are first used, and the finite-size e¤ects on the
deconfinement phase transition are investigated by probing the behavior of some useful
quantities near the transitionfi It turns out that in a finite size system, all singularities
occurring in the thermodynamic limit are smeared out and the transition is perfectly
smooth.
Secondly, the color-singletness requirement is imposed to the QGP phase, to satisfy
the color confinement property of QCD, introducing an additional finite-size e¤ect, and
leading to a shift of the transition pointfi A finite size scaling analysis is then carried out
to determine the scaling critical exponents, characterizing the scaling behavior when
approaching the thermodynamic limit (V ��! 1), both in analytical and numerical
ways.
Since hadrons are not pointlike because of their composite character, they should
be treated as extended particlesfi To account for this, we then consider the excluded
volume e¤ects and examine their e¤ects on the deconfinement phase transitionfi
The first chapter of this thesis is devoted to a review of the physics of phase transi-
tions, as well as their classification, and the second one overviews the phase transitions
in finite systems.
In the third chapter, we study the deconfinement phase transition in a finite system
within the phase coexistence modelfi Equations of state of infinite matter are used
for a hadronic gas of pions and for a QGP consisting of gluons and massless quarks,
then the color-singletness condition is implemented using the projection method. An
approximate color-singlet partition function of the QGP is derived within the saddle
point approximation and is used in a first step to calculate mean values of physical
quantitiesfi The expressions of these latter with T, _ and V are obtained, in these two
cases, and both temperature-driven and density-driven deconfinement phase transitions
are then studied, at fixed chemical potential and temperature respectivelyfi In a second
step, the exact integral expression of the color-singlet partition function of the QGP
is used to accurately determine mean values of several quantities probing the phase
transition in a finite volume, without explicitly calculating the color-singlet partition
function itself.
The fourth chapter is dedicated to the numerical determination of the scaling critical
exponents characterizing the studied phase transition, by the mean of a finite size
scaling analysis.
In the fifth chapter, the excluded volume correction is considered for the hadronic
phase, and his e¤ects on the deconfinement phase transition are investigatedfi
Last, the obtained results are discussed and compared to results of other models
and approaches.